QC 


UC-NBLF 


ROE  AND  LABOR 

UEODETIU    SURVEY 

O.  H.  TITTMANN. 


DIRECTIONS 

FOR 

MAGNETIC  MEASUREMENTS 


BY 


DANIEL  L.  HAZARD 

COMPUTER,    DIVISION   OF  TERRESTRIAL  MAGNETISM 


WASHINGTON 

GOVERNMENT  PRINTING   OFFICE 
,  1911 


GIFT  OF 


DEPARTMENT  OF  COMMERCE  AND  LABOR 

M   ^  COAST    AND    GEODETIC    SURVEY 
O.  H.  TITTMANN,  SUPERINTENDENT 


DIRECTIONS 

FOR 

MAGNETIC  MEASUREMENTS 


BY 


DANIEL  L.  HAZARD 

COMPUTER,    DIVISION    OF  TERRESTRIAL   MAGNETISM 


WASHINGTON 

GOVERNMENT  PRINTING  OFFICE 
1911 


OF  THE 

UNIVERSITY 


.- 


or, 


CONTENTS. 


Page. 

Preface 5 

THEORY  or  MAGNETIC  MEASUREMENTS. 

The  earth's  magnetism 7 

Introduction 7 

Magnetic  elements 7 

Units  of  measure  of  intensity 8 

Distribution  of  the  earth's  magnetism 8 

Variations  of  the  earth's  magnetism 9 

Derivation  of  formulas 10 

Determination  of  the  true  meridian  by  observations  of  the  sun 10 

Dip '. 12 

Horizontal  intensity 14 

Oscillations 15 

Deflections 17 

Total  intensity 21 

Determination  of  the  constants  of  a  magnetometer 23 

Moment  of  inertia 23 

Temperature  coefficient 26 

Induction  coefficient 28 

Distribution  coefficients 30 

Deflection  distances 34 

DIRECTIONS  FOR  MAGNETIC  OBSERVATIONS  ON  LAND. 

General  directions 35 

Equipment 39 

Latitude  from  observations  of  the  sun 40 

Latitude  from  observations  of  Polaris 44 

Determination  of  the  true  meridian  and  local  mean  time  by  observations  of 

the  sun 45 

Adjustment  of  the  theodolite 45 

Observations 47 

Computation 50 

Determination  of  the  true  meridian  by  observations  of  Polaris 52 

Determination  of  the  magnetic  declination *  53 

A .  With  a  'magnetometer 53 

Coast  and  Geodetic  Survey  pattern 53 

India  Magnetic  Survey  pattern 59 

Declination  from  horizontal  intensity  observations 61 

B.  With  a  compass  declinometer  or  compass  attachment  of  a  dip  circle.  62 
Determination  of  the  dip 66 

A.  With  a  dip  circle 66 

B.  With  an  earth  inductor 72 

Determination  of  the  horizontal  intensity 74 

Torsion  observations '. 74 

Oscillations 74 

Deflections 75 

Computation 78 

Determination  of  the  total  intensity. 81 

3 


345597 


4  \/  ;  lC\  ;  v      CONTENTS. 

DlREC?}  OJJS  .fSpa  ;Q^£\AT10N&   AT'  SEA  . 


.•:.  .  /.*.  :  :  ?.-       !'."  .......................................  87 

Decimation  .............  :  .............................................  88 

Dip  and  total  intensity  .................................................  97 

Special  directions  ......................................................  102 

DIRECTIONS  FOR  OPERATING  A  MAGNETIC  OBSERVATORY. 

Buildings  ..............................................................  103 

Variation  instruments.  .  ................................................  103 

Conversion  to  absolute  values  ...........................................  106 

Base-line  values  ...................................................  107 

Scale  values  ......................................................  109 

Temperature  coefficients  ...........................................  113 

Temperature  ...........................................................  114 

Time  scale  ...........  ..........................  ........................  115 

Reading  of  ordinates  ....................................................  115 

Programme  of  work  ....................................................  115 

General  directions  ......................................................  116 

TABLES. 

I.  Correction  to  the  observed  altitude  of  the  sun  for  refraction  and  parallax.  .  119 

II.  Correction  in  azimuth  and  altitude  of  the  sun  for  semi-diameter  ........  120 

III.  Latitude  from  circum-meridian  altitudes  of  the  sun;  values  of  m  ........  120 

IV.  Latitude  from  circum-meridian  altitudes  of  the  sun;  values  of  A  ........  121 

V.  Correction  for  rate  of  chronometer.     (Oscillations)  .....................  126 

VI.  Torsion  factor.     (Oscillations)  .........................................  126 

VII.  Reduction  of  log  C  from  20°  C.  to  other  temperatures.     (Deflections)  ____  127 

VIII.  Correction  for  lack  of  balance  of  dip  needle  ...........................  127 

IX.  Diurnal  variation  of  declination  ......................................  128 

X.  Diurnal  variation  of  dip  ..............................................  129 

XI.  Diurnal  variation  of  horizontal  intensity  ...............................  130 

XII.  Multiples  of  the  sines  of  the  angles  22°.  5,  45°,  and  67°.  5  ................  131 

ILLUSTRATIONS. 

FIG.  1  .  Fundamental  spherical  triangle  .....................................  11 

2.  Position  of  magnets  during  deflections  ........  ........................  18 

3.  Coast  and  Geodetic  Survey  pattern  magnetometer  .....................  54 

4.  India  Magnetic  Survey  pattern  magnetometer  ........................  59 

5.  Kew  pattern  dip  circle  .............................................  67 

.6.  Remagnetization  of  dip  needle  .......................................  68 

7.  Wild  pattern  earth  inductor  .........................................  72 

8.  Four  and  six  oscillations  ............................................  75 

9.  Lloyd-Creak  pattern  dip  circle  ......................................  98 

10.  Relative  position  of  variometers  .....................................  104 


DIRECTIONS  FOR  MAGNETIC  MEASUREMENTS. 


PREFACE. 

Although  the  principles  involved  in  the  measurements  of  the  earth's 
magnetism  have  not  changed  since  the  publication  of  the  third 
edition  of  "Directions  for  Magnetic  Observations  with  Portable 
Instruments,"  *  the  methods  of  observing  and  the  instruments 
used  have  received  so  many  modifications  as  the  result  of  accumu- 
lated experience  that  a  new  presentation  of  the  subject  has  been 
needed  for  some  time  to  facilitate  the  field  work  and  to  secure 
uniformity.  In  addition  it  is  important  that  the  principles  involved 
should  be  explained  in  more  detail  than  was  done  in  the  above- 
mentioned  publication,  so  that  the  observer  may  have  a  better  under- 
standing of  what  he  is  doing  and  why  he  is  doing  it  without  being 
obliged  to  refer  to  other  publications.  Moreover,  with  the  estab- 
lishment of  five  magnetic  observatories  and  the  inauguration  of 
magnetic  observations  on  board  the  vessels  of  the  Survey,  the  need 
has  arisen  for  printed  directions  for  making  the  observations  required 
in  those  two  branches  of  the  magnetic  work  of  the  Survey.  The 
endeavor  will  be  made  to  present  the  subject-matter  in  such  form 
that  an  observer  familiar  with  the  use  of  instruments  of  precision 
but  without  experience  in  magnetic  work  may  be  able  to  make  in  a 
satisfactory  manner  the  various  observations  incident  to  the  deter- 
mination of  the  magnetic  elements  without  other  assistance  than  that 
to  be  obtained  from  these  directions. 

In  the  preparation  of  this  paper  the  following  publications  have 
been  consulted: 

Principal  Facts  of  the  Earth's  Magnetism,  by  L.  A.  Bauer.  Wash- 
ington, Government  Printing  Office,  1909.  (Reprinted  from  U.  S. 
Magnetic  Declination  Tables,  1902.) 

Theory  of  Magnetic  Measurements,  by  F.  E.  Nipher.  New  York, 
1886. 

Spherical  and  Practical  Astronomy,  by  Wm.  Chauvenet.  Phila- 
delphia, 1887. 

Traite  de  Magnetisme  Terrestre,  by  E.  Mascart.     Paris,  1900. 

Erdmagrietismus,  Erdstrom  und  Polarlicht,  by  Dr.  A.  Nippoldt,  jr. 
Leipzig,  1903. 

*Appendix  No.  8,  C.  &  G.  S.  Report  for  1881.    Gov't  Printing  Office,  1882. 


6  DIRECTIONS  FOB  MAGNETIC   MEASUREMENTS. 

Handbuch  des  Erdmagnetismus,  by  J.  Lament.     Berlin,  1849. 

Ableitung  des  Ausdrucks  fur  die  Ablenkung  eines  Magnetnadel 
durch  einen  Magnet,  by  Dr.  Borgen.  Hamburg,  1891. 

Collimator  Magnets  and  the  Determination  of  the  Earth's  Hori- 
zontal Force,  by  Charles  Chree.  Proceedings  Roy.  Soc.  London, 
No.  419,  1899. 

The  Law  of  Action  between  Magnets,  by  Charles  Chree.  London, 
Edinburgh,  and  Dublin,  Phil.  Magazine,  August,  1904. 

La  Section  MagnStique  de  Tobservatoire  de  1' fibre,  by  E.  Merveille, 
S.  J.  Barcelone,  1908. 

Elementary  Practical  Physics,  by  Stewart  and  Gee.  London, 
1887. 

Elements  of  the  Mathematical  Theory  of  Electricity  and  Mag- 
netism, by  J.  J.  Thomson,  Cambridge,  England,  1897. 

A  Treatise  on  Magnetism  and  Electricity,  by  Andrew  Gray. 
London,  1898. 

A  Physical  Treatise  on  Electricity  and  Magnetism,  by  J.  E.  H. 
Gordon.  New  York,  1880. 

Practical  Problems  and  the  Compensation  of  the  Compass,  by 
Diehl  and  Southerland.  Washington,  Government  Printing  Office, 
1898. 

Admiralty  Manual  for  the  Deviation  of  the  Compass,  by  Evans 
and  Smith.  London,  1901. 

The  subject  will  be  treated  under  the  following  general  headings: 

I.  Theory  of  magnetic  measurements,  including  some  of  the  more 
important   facts   about   the   earth's    magnetism   and    the   methods 
employed  for  determining  instrumental  constants. 

II.  Directions  for  absolute  observations  on  land. 

III.  Directions  for  observations  at  sea. 

IV.  Directions  for  operating  a  magnetic  observatory. 


THEORY  OF  MAGNETIC  MEASUREMENTS. 


THE  EARTH'S  MAGNETISM. 
INTRODUCTION. 

Whether  the  earth  is  a  great  magnet  or  simply  acts  as  a  magnet 
as  the  result  of  electric  currents  flowing  about  it,  it  is  surrounded  by 
a  magnetic  field,  and  the  measurements  of  the  earth's  magnetism  at 
any  place  consist  in  determining  the  direction  and  intensity  of  that 
field. 

A  magnet  suspended  in  such  a  way  as  to  be  free  to  turn  about  its 
center  of  gravity  would  take  a  position  with  its  magnetic  axis  tangent 
to  the  lines  of  force  of  the  earth's  magnetic  field.  As  it  is  practically 
impossible  to  suspend  a  magnet  in  that  way,  it  is  usual  to  determine 
the  direction  of  the  earth's  magnetic  field  by  means  of  two  magnets, 
one  constrained  to  rotate  in  a  horizontal  plane  and  the  other  in  a 
vertical  plane. 

MAGNETIC    ELEMENTS. 

The  magnetic  meridian  at  any  place  is  the  vertical  plane  defined 
by  the  direction  of  the  lines  of  force  at  that  place. 

The  magnetic  declination,  Dt  is  the  angle  between  the  astronomic 
meridian  and  the  magnetic  meridian  and  is  considered  East  or  West 
according  as  the  magnetic  meridian  is  east  or  west  of  true  North. 
Declination  is  often  called  variation  of  the  compass  or  simply  variation. 

The  dip  or  inclination,  I,  is  the  angle  which  the  lines  of  force  make 
with  the  horizontal  plane. 

Instead  of  measuring  the  total  intensity,  F,  of  the  earth's  magnetic 
field,  it  is  usually  more  convenient  to  measure  its  horizontal  com- 
ponent, H.  These  three  quantities,  declination,  dip,  and  horizontal 
intensity,  are  usually  spoken  of  as  the  magnetic  elements  and  from 
them  the  total  intensity  and  its  components  in  the  three  coordinate 
planes  may  be  computed  by  means  of  the  simple  formulas: 

F=H  sec  I  Y  =  H  sin  D 

X  =  H  cos  D  Z  =  H  tan  7 

X  and  Y  being  the  components  in  the  horizontal  plane,  X  directed 
north  (  +  )  or  south  (  — )  and  Y  directed  east  (  +  )  or  west  (  — ),  and 
Z  being  the  component  directed  vertical!}'  downward. 


8  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

UNITS    OF   MEASURE    OF   INTENSITY. 

The  intensity  of  a  magnetic  field  is  the  force  which  a  unit  pole 
would  experience  when  placed  in  it.  A  unit  pole  is  one  which  repels 
an  equal  pole  at  unit  distance  with  unit  force. 

At  the  present  time  almost  all  measurements  of  the  intensity  of 
the  earth's  magnetic  field  are  made  in  terms  of  the  C.  G.  S.  system, 
in  which  the  fundamental  units  are  the  centimeter,  the  gram,  and  the 
second.  Before  the  metric  system  came  into  general  use,  it  was 
customary  in  English-speaking  countries  to  use  the  British  system  of 
units,  based  on  the  foot,  the  grain,  and  the  second.  To  convert 
measures  of  intensity  expressed  in  British  units  into  their  equivalents 
in  the  C.  G.  S.  system,  they  must  be  multiplied  by  the  factor  0.046108 
(logarithm  =  8.66378). 

DISTRIBUTION    OF   THE    EARTH 's   MAGNETISM. 

The  magnetic  poles  of  the  earth  are  those  points  on  its  surface  at 
which  the  dip  needle  stands  vertical  and  toward  which  the  compass 
needle  points,  throughout  the  adjacent  region.  The  north  magnetic 
pole  is  approximately  in  latitude  70°  N.  and  longitude  97°  W., 
and  the  south  magnetic  pole  in  latitude  73°  S.  and  longitude  156°  E. 
It  must  be  borne  in  mind  that  these  magnetic  poles  have  not  the 
characteristics  of  the  poles  of  a  bar  magnet.  If  they  had,  there 
should  be  an  enormous  increase  in  the  total  intensity  when  approach- 
ing the  poles,  which  is  not  the  case.  They  are  not  even  the  points 
of  maximum  intensity,  there  being  four  areas,  two  in  each  hemis- 
phere, in  which  the  total  intensity  is  greater.  The  earth  acts  like  a 
great  spherical  magnet;  that  is,  a  bar  magnet  at  its  center  which 
would  produce  the  effects  observed  at  the  surface  would  have  its 
poles  practically  coincident. 

If  the  earth  were  uniformly  magnetized,  its  magnetic  poles  would 
be  at  the  opposite  extremities  of  a  diameter,  the  magnetic  meridians 
would  be  arcs  of  great  circles,  and  a  comparatively  small  number  of 
observations  would  suffice  to  determine  the  distribution  of  mag- 
netism over  its  surface.  As  a  matter  of  fact,  according  to  Bauer, 
only  about  two-thirds  of  the  earth's  magnetism  can  be  represented 
by  a  uniform  magnetization  and  the  distribution  of  the  remainder  is 
very  irregular,  representing  the  resultant  effect  of  irregularities  which 
are  continental,  regional,  or  purely  local  in  extent.  These  local 
irregularities  or  " local  disturbances"  are  sometimes  of  sufficient 
intensity  to  produce  local  magnetic  poles,  such  as  have  been  found  by 
observation  near  Juneau,  Alaska,  and  between  Kursk  and  Odessa, 
in  Russia. 

It  is  usual  to  represent  the  distribution  of  the  earth's  magnetism 
graphically  by  means  of  isogonic,  isoclinic,  and  iso-dynamic  charts, 


THE  EARTH'S  MAGNETISM.  9 


on  which  are  shown  lines  of  equal  declination,  equal  inclination,  or 
equal  intensity.  For  the  construction  of  such  charts  many  observa- 
tions are  required  in  order  that  the  irregular  distribution  may  be 
represented  properly, "and  it  is  the  usual  experience  that  the  addition 
of  new  observations  brings  out  new  irregularities.  Inasmuch  as  the 
earth's  magnetism  is  undergoing  constant  change,  its  distribution  is 
different  for  different  epochs,  and  a  knowledge  of  the  amount  of 
change  from  one  year  to  another  is  necessary  before  the  results  of 
observations  made  at  different  times  can  be  reduced  to  the  year  for 
which  it  is  desired  to  construct  an  iso-magnetic  chart. 

VARIATIONS    OF   THE    EARTH'S    MAGNETISM. 

The  continual  change  to  which  the  earth's  magnetism  is  subject 
has  been  analyzed  in  various  ways  and  shown  to  be  the  resultant 
effect  of  several  more  or  less  systematic  variations  combined  with 
irregular  disturbances,  which  from  time  to  time  attain  considerable 
magnitude^  constituting  what  are  known  as  magnetic  storms.  These 
" storms"  occur  at  irregular  intervals  and  may  last  only  a  few  hours 
or  several  days  and  sometimes  attain  an  intensity  sufficient  to  pro- 
duce a  range  of  1°  or  2°  in  declination  and  of  2  or  3  per  cent  in  the 
horizontal  intensity.  They  usually  occur  almost  simultaneously  over 
the  entire  surface  of  the  globe,  and  often  accompany  auroral  displays 
and  the  appearance  of  large  spots  on  the  sun.  The  occurrence  of  a 
storm  during  observations  can  usually  be  detected  by  the  erratic 
behavior  of  the  magnet  or  needle,  and  calls  for  a  repetition  of  the 
observations  after  the  storm  has  subsided. 

Of  the  systematic  variations  the  largest  and  most  important  is  the 
secular  variation,  so  called  because  it  requires  centuries  for  its  full 
development.  While  magnetic  observations  do  not  as  yet  cover  a 
sufficiently  long  term  of  years  to  warrant  a  definite  conclusion,  yet 
the  evidence  is  strong  that  at  least  for  the  direction  of  the  earth's 
field  the  secular  variation  is  of  a  periodic  character,  i.  e.,  that  the 
change  with  lapse  of  time  does  not  go  on  indefinitely  in  one  direction. 
Eventually  a  turning  point  is  reached.  In  the  case  of  the  declina- 
tion, numerous  series  of  observations  are  available  which  are  of 
sufficient  extent  to  include  one  and  in  some  cases  probably  two  such 
turning  points.  Tables  showing  the  secular  change  of  the  magnetic 
elements  in  the  United  States  will  be  found  on  pages  114-119  of 
"United  States  Magnetic  Tables  and  Magnetic  Charts  for  1905." 

Of  the  periodic  variations  having  for  periods  a  year,  a  solar  day 
and  a  lunar  day,  the  only  one  of  sufficient  magnitude  to  be  of  prac- 
tical importance  is  the  solar-diurnal  variation,  or  as  it  is  usually 
designated,  diurnal  variation.  Tables  IX,  X,  and  XI  show  the 
diurnal  variation  of  declination,  dip,  and  horizontal  intensity  at  four 
of  the  magnetic  observatories  of  the  Coast  and  Geodetic  Survey, 
based  upon  several  years'  observations.  They  were  condensed  from 


10  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

tables  giving  the  average  diurnal  variation  for  10  selected  days  for 
each  month  of  the  years  specified. 

The  diurnal  variation  appears  to  be  closely  associated  with  the 
position  of  the  sun  above  the  horizon.  During*  the  night  hours  there 
is  normally  little  change  in  any  of  the  three  elements.  The  daily 
range  is  greater  in  years  of  maximum  sun  spot  frequency  than  in 
years  of  minimum,  and  varies  somewhat  with  the  season. 

From  an  inspection  of  Table  IX  it  will  be  seen  that  for  all  of  the 
observatories  the  diurnal  variation  of  declination  shows  the  same 
general  characteristics;  a  well-marked  maximum  (easterly  extreme) 
between  8  and  10  in  the  morning,  and  a  well-marked  minimum  (west- 
erly extreme)  between  1  and  3  in  the  afternoon. 

For  dip  and  horizontal  intensity,  on  the  other  hand,  there  is  only 
one  well-marked  extreme,  except  in  the  case  of  the  summer  months 
at  Cheltenham,  and  even  there  one  extreme  is  much  more  pronounced 
than  the  other.  In  all  cases  this  extreme  occurs  not  far  from  noon, 
but  at  Sitka  and  Cheltenham  it  is  a  maximum  for  dip  and  a  minimum 
for  horizontal  intensity,  while  for  Honolulu  and  Porto  Rico  it  is  a 
minimum  for  dip  and  a  maximum  for  horizontal  intensity. 

DERIVATION  OF  FORMULAS. 

DETERMINATION    OF   THE   TRUE    MERIDIAN    BY    OBSERVATIONS   OF    THE 

SUN. 

As  the  magnetic  declination  is  the  angle  between  the  true  meridian 
and  the  magnetic  meridian,  its  measurement  requires  the  determina- 
tion of  the  direction  of  both  of  these  planes.  The  direction  of  the 
magnetic  meridian  is  obtained  by  means  of  a  magnet  free  to  rotate 
in  a  horizontal  plane  about  a  vertical  axis.  The  direction  of  the  true 
meridian  may  be  determined  by  observations  either  of  the  sun  or  of 
a  star,  especially  Polaris.  In  connection  with  magnetic  work  it  is 
usually  more  convenient  to  make  the  observations  in  the  daytime 
and  the  method  in  general  use  consists  of  a  series  of  observations  of 
the  sun  both  morning  and  afternoon,  each  observation  comprising  a 
measure  of  the  altitude  of  the  sun  and  the  angle  between  it  and  a 
reference  (azimuth)  mark,  and  a  record  of  the  time.  The  computa- 
tion of  the  azimuth  of  the  sun  and  the  local  mean  time  from  observa- 
tions of  this  character  involves  the  solution  of  the  spherical  triangle 
defined  by  the  pole,  the  zenith,  and  the  sun,  the  three  sides  being 
known.  The  fundamental  formulas  of  spherical  trigonometry  have 
been  transformed  to  fit  this  special  case  as  follows : 

When  the  sides  of  a  spherical  triangle  are  known  the  angles  may  be 
computed  by  formulas  of  the  form: 


sin  s1  sin  (sl  —  a) 
in  which  2sl  =  a  +  b  +  c. 


DERIVATION   OF   FORMULAS. 


11 


In  Figure  1  let  Z  P  S  represent  the  triangle  defined  by  the  zenith, 
the  pole,  and  the  sun. 

SP  =  a  =  90°-£  =  2?    given    in 
the  Ephemeris  of  the  sun. 

SZ  =  6  =  90°  -  h       determined 
by  observation. 

PZ  =  c  =  90°  -  <£       determined 
by  observation. 

The  angle  SZP  =  Anis  the  angle 
between  the  true  meridian  and  the 
vertical  plane  through  the  sun  and 
is  therefore  the  azimuth  of  the  sun 
counted  from  the  North.  The 
angle  SPZ  =  B  is  the  hour  angle  of 
the  sun,  t.  Substituting  the  values 

.  ;  .  -0  . 

or  a,  o,  and  c  in  the  tormina  and 

letting  2s  =  p-\-Ji  +  (j))  the  following  transformations  may  be  made  : 

-7i-  <  =  180 


FIG.  1.—  Fundamental  spherical  triangle. 


COS  S  COS  (S—p) 

As  it   is   usual   to  reckon   azimuths  from   the  south,  substitute 

180°  -A,  =  An 
and  the  equation  may  be  written  in  the  form: 

ctn2-Jk48  =  sec  s  sec  (s  —  p)  sin  (s—(f>)  sin  (s  —  Ji) 
A  similar  transformation  of  the  equation  for  the  angle  B  =  t  gives 

tan2 4-  2  =  cos  s  sin  (s  —  h)  esc  (s  —  (j))  sec  (s  —  p) 
and  by  combination  with  the  equation  for  ctn2JJLs: 

tan2i*  =  F1 
and 

tan  4- 1  = 


sin  (s  —  Ji)  sec  (s  —  p) 
ctn  iA, 


a  very  convenient  form  when  the  azimuth  and  hour  angle  are  to  be 
computed  from  the  same  set  of  observations. 


12  DIRECTIONS   FOE   MAGNETIC    MEASUREMENTS. 

The  computed  angle  between  the  sun  and  the  true  south  meridian 
combined  with  the  measured  angle  between  the  sun  and  a  selected 
terrestrial  object  (azimuth  mark)  gives  the  angle  between  the  true 
south  meridian  and  the  mark,  or  the  true  azimuth  of  the  mark. 

The  computed  hour  angle  of  the  sun  combined  with  the  equation  of 
time  gives  the  local  mean  time  of  observation,  and  this  compared 
with  the  chronometer  time  of  observation  gives  the  chronometer 
correction  on  local  mean  time.  If  the  chronometer  correction  on 
standard  time  has  been  determined  by  means  of  telegraphic  time 
signals,  an  approximate  value  of  the  longitude  of  the  place  can 
readily  be  computed. 

DIP. 

The  dip  is  usually  measured  by  means  of  a  dip  circle  in  which  a 
magnetized  needle  is  supported  so  as  to  be  free  to  rotate  in  a  vertical 
plane.  A  steel  axle  through  the  center  of  gravity  of  the  needle  ter- 
minates in  finely  ground  pivots  which  rest  on  agate  knife  edges.  The 
angle  of  dip  is  measured  on  a  graduated  circle  concentric  with  the 
axle  of  the  needle.  In  order  to  measure  the  angle  of  dip  directly,  the 
needle  must  swing  in  the  magnetic  meridian.  The  observed  angle 
of  inclination  in  any  other  plane  will  be  too  large,  as  will  be  seen  from 
the  following  considerations.  In  the  magnetic  meridian  the  hori- 
zontal and  vertical  components  of  the  total  intensity  are  H  and  Z, 
and  Z  =  77  tan  7.  In  a  plane  making  an  angle  a  with  the  magnetic 
meridian,  the  components  are  H  cos  a  and  Z,  and  Z  =  H  cos  a  tan  Ia. 
Hence  tan  7=  cos  a  tan  7a.  As  the  cosine  of  an  angle  is  always  los 
than  unity,  7a  is  always  greater  than  7.  This  formula  may  be  used  to 
compute  the  true  dip  from  observations  out  of  the  meridian,  provided 
the  angle  a  is  known.  The  equation  may  be  written  in  the  form 
ctn7a  =  ctn7  cos^.  Let  <r  =  90°;  then  ctn7a  =  0  and  7a  =  90°.  That 
is,  when  the  instrument  is  in  the  magnetic  prime  vertical  the  dip 
needle  stands  vertical,  a  fact  wrhich  furnishes  a  simple  method  for 
setting  the  instrument  in  the  magnetic  meridian  when  a  compass 
attachment  is  not  available  for  the  purpose.  Extreme  accuracy  in 
the  determination  of  the  magnetic  meridian  is  not  required,  as  will 
be  seen  if  a  be  computed  from  the  above  formula  assuming  7=45° 
and  Ia=  45°  OOM,  the  resulting  value  of  a  being  37'.  That  is,  unless 
the  instrument  is  more  than  30 '  out  of  the  magnetic  meridian,  the 
effect  on  the  dip  is  not  as  much  as  O'.l. 

The  true  dip  may  be  obtained  by  combining  observations  in  two 
planes  at  right  angles  to  each  other. 

For  Ctn  Ta  =  ctn  7  cos  a 

and  ctn  7(9o°-a)  =  ctn  7  cos  (90  —  a)  =  ctn  7  sin  a 

Hence  ctn  27a  +  ctn  27(9o°_a)  =  ctn  27 


DERIVATION   OF   FORMULAS.  13 

The  ideal  dip-needle  would  be  perfectly  symmetrical  in  size  and 
mass  with  respect  to  the  axis  of  its  pivots,  but  this  condition  can  not 
be  exactly  attained  by  the  maker,  and  subsequent  use  of  the  needle 
is  liable  to  increase  the  divergence  from  this  ideal  condition.  Most 
of  the  errors  due  to  lack  of  symmetry  and  adjustment  are  eliminated 
by  reversal  of  instrument  and  needle  and  reversal  of  the  polarity  of 
the  needle.  Yet  it  will  usually  be  found  that  different  values  of  dip 
are  obtained  before  and  after  reversing  polarity,  indicating  that  the 
needle  would  not  exactly  balance  if  demagnetized.  This  lack  of  bal- 
ance may  be  ascribed  without  material  error  *  to  a  small  weight  p 
in  the  longitudinal  axis  of  the  needle  at  a  distance  d  from  the  axis  of 
the  pivots.  The  equations  of  equilibrium  before  and  after  reversal 
of  polarities  will  be: 

pd  cos  In  =  FM  sin  (/—  In) 
and  pd  cos  Is  =  FM  sin  (/,  -  /) 

assuming  that  the  magnetic  "moment  M  of  the  needle  is  the  same 
before  and  after  reversal. 

Hence  cos  7TO_  sin  (/  —  /„)_  sin  I  cos  In  —  cos  /  sin  In 

cos  Is    sin(7s  —  I)      sin  Is  cos  7  —cos  Is  sin  I 

Clearing  of  fractions  and  dividing  by  cos  Is  cos  In  cos  7, 
tan  Ig  —  tan  1=  tan  /  —  tan  In 
tan  1=  to*J*^d* 

That  is,  where  the  observations  give  different  values  of  dip  before 
and  after  reversal  of  polarities,  the  mean  of  the  two  quantities  does 
not  give  the  true  dip.  Instead,  the  angle  must  be  found  whose 
tangent  is  the  mean  of  the  tangents  of  the  observed  angles.  To 
avoid  the  necessity  of  making  this  computation  for  each  observation, 
Table  VIII  has  been  prepared,  giving  the  correction  required  by  the 
dip  obtained  by  using  the  formula 

T   4  + A 
2 

For  example,  if  the  observed  dip  was  72°  15'.0  before  reversal 
of  polarities  and  72°  45 '.0  afterwards,  the  true  dip  would  be 
72°30/.0  +  0'.2  =  72°  3Q'.2. 

At  a  magnetic  observatory  an  earth  inductor  is  usually  provided  for 
determining  the  dip.  With  this  instrument  more  accurate  results 
may  be  obtained  in  less  time  than  with  a  dip  circle.  The  operation 
of  the  earth  inductor  is  based  on  the  principle  that  when  a  closed 
circuit  is  revolved  in  a  magnetic  field,  electric  currents  are  induced 
unless  the  axis  of  rotation  is  tangent  to  the  lines  of  force  of  the  field. 

*  The  needle  is  so  long  compared  with  its  width  that  the  lack  of  symmetry  with  respect  to  the  longitudinal 
axis  is  not  apt  to  be  appreciable. 


14  DIRECTIONS   FOE  MAGNETIC   MEASUREMENTS. 

After  the  instrument  has  been  leveled  and  placed  with  the  axis  of 
rotation  in  the  magnetic  meridian,  the  coil  is  rotated  and  its  inclina- 
tion is  changed  until  the  induced  current  becomes  zero  as  shown  by 
a  galvanometer  placed  in  the  circuit.  The  angle  of  inclination  of  the 
coil,  or  dip,  is  then  read  off  on  the  vertical  circle. 

Numerous  comparisons  of  dip  circles  with  each  other  and  with  earth 
inductors  have  established  the  fact  that,  in  spite  of  every  refinement 
of  adjustment  and  care  in  observing,  different  dip  circles  give  differ- 
ent results  and  nearly  all  require  corrections  to  reduce  to  the  more 
accurate  earth  inductor  results.  This  is  probably  due  in  many  cases 
to  irregularity  of  pivots  of  the  needles  and  sometimes  to  slight 
impurities  in  the  metal  entering  into  the  make-up  of  the  instrument. 
While  the  effect  of  either  of  these  causes  would  be  different  for  differ- 
ent angles  of  dip,  it  is  the  practice  in  the  Coast  and  Geodetic  Survey 
to  assume  a  uniform  correction  for  the  limited  range  of  dip  involved 
in  a  season's  work. 

In  the  case  of  two  dip  circles  which  were  used  over  a  wide  range  of 
dip  and  showed  large  and  variable  corrections,  analytical  expressions 
of  the  form 

sin  I  ,     cos  / 

-p-+* 


were  derived,  from  which  to  compute  the  required  corrections,  based 
on  the  assumption  that  the  varying  corrections  were  to  be  ascribed 
to  the  effect  of  the  metal  composing  the  instrument. 

HORIZONTAL   INTENSITY. 

Up  to  the  time  of  Gauss  all  measures  of  horizontal  intensity  were 
relative,  and  consisted  in  comparing  the  times  of  oscillation  at  differ- 
ent places  of  a  magnet  rotating  in  the  horizontal  plane  about  a  ver- 
tical axis.  Assuming  the  magnetic  moment  of  the  magnet  to  be  con- 
stant, the  horizontal  intensity  is  inversely  proportional  to  the  square 
of  the  time  of  oscillation.  As  a  matter  of  fact,  all  magnets  tend  to 
lose  their  magnetism  gradually,  but  this  decrease  of  magnetic  moment 
was  determined  and  allowed  for  approximately  by  observing  at  a 
base  station  both  at  the  beginning  and  end  of  a  voyage  or  a  season's 
work. 

Gauss  conceived  the  idea  of  combining  with  the  oscillations  a  set  of 
observations  in  which  the  intensity  magnet  is  used  to  deflect  an 
auxiliary  magnet,  and  thus  determine  the  horizontal  intensity  abso- 
lutely, and  this  is  the  method  in  general  use  at  the  present  day.  Two 
distinct  operations  are  involved:  Oscillations,  which  serve  to  deter- 
mine the  product  of  the  magnetic  moment  of  the  magnet  and  the 
horizontal  intensity;  deflections,  from  which  the  ratio  of  the  same 
two  quantities  is  obtained. 


DERIVATION   OF   FORMULAS.  15 


OSCILLATIONS. 


If  a  magnet  be  free  to  rotate  about  a  vertical  axis  through  its  center 
of  gravity,  it  will  come  to  rest  with  its  magnetic  axis  in  the  magnetic 
meridian.  If  it  be  turned  out  of  that  plane  and  then  released  it  will 
oscillate  as  a  horizontal  pendulum  under  the  influence  of  the  earth's 
magnetism,  the  amplitude  of  its  swing  gradually  diminishing  until  it 
finally  comes  to  rest  again  in  the  magnetic  meridian.  If  T  be  the 
time  of  one  oscillation;  i.  e.,  the  time  between  two  successive  transits 
(in  opposite  directions)  across  the  meridian,  K  the  combined  moment 
of  inertia  of  the  magnet  and  stirrup  about  the  axis  of  rotation,  and 
M  the  magnetic  moment  of  the  magnet,  the  equation  of  motion  for  a 
pendulum  becomes: 


0.00000 
02 


3  04 

4 


5 


12 


subject,  however,  to  certain  corrections  as  explained  below. 

Reduction  to  infinitesimal  arc.  —  The  above  formula  is  based  on  the 
assumption  that  the  arc  of  vibration  is  infinitesimal.  For  a  finite 
arc  the  observed  time  of  one  oscillation  must  be  diminished  by  a 

small   amount,    the   corrective   factor   being   (1  —  ^-  V   in   which 

a'  and  a,"  are  the  initial  and  terminal  arcs  of  vibration,  expressed  in 

(a2\ 
1  —  ^j  \  a  being  the  average   arc   of  vibration. 

From  the  adjoining  table  it  will  be  seen  that  for  an 
average  arc  of  3°  this  correction  amounts  to  only  1 
part  in  25000,  and  as  the  arc  of  vibration  need  never 
exceed  this  amount,  and  in  the  majority  of  magnet- 
ometers is  still  more  restricted  by  the  limits  of  the 
scale  of  the  magnet,  this  correction  is  in  general 
negligible. 

Correction  for  rate  of  chronometer.  —  The  observed  time  of  one  oscil- 
lation must  be  corrected  for  the  rate  of  the  chronometer  used.  If  r 
be  the  daily  rate  of  the  chronometer  in  seconds,  plus  when  losing  and 
minus  when  gaining,  the  observed  value  of  T  must  be  multiplied  by 

the  factor  (  1  +     r     ")  or    T  must  be   increased    by    0.00001  16  Tr. 
\       8o400/ 

Values  of  this  expression  for  different  values  of  T  and  r  are  given  in 
Table  V. 

Correction  for  torsion.  —  The  earth's  magnetism  is  not  the  only  force 
acting  to  cause  the  oscillations.  It  is  usual  to  suspend  the  magnet 
by  one  or  more  silk  fibers  or  by  a  very  fine  wire  or  metallic  ribbon, 
the  torsion  of  which  must  be  taken  into  account.  The  ratio  between 
the  force  of  torsion  and  the  horizontal  intensity  may  be  determined 
in  the  following  manner  :  When  the  magnet  is  at  rest  in  the  magnetic 


16  DIRECTIONS   FOR    MAGNETIC    MEASUREMENTS. 

meridian,  if  the  upper  end  of  the  suspension  fiber  be  turned  through 
any  angle,  say  90°,  the  magnet  will  be  turned  out  of  the  meridian 
through  a  small  angle  h  (expressed  in  minutes)  on  account  of  the  tor- 
sion of  the  fiber.  The  equation  of  equilibrium  between  the  two 
forces  for  a  twist  of  90°  is: 

C  (5400  -h)=MHsmh        or  C=   ^^  y 


in  which  C  is  the  force  of  torsion  per  minute  of  arc.  Experiments 
have  shown  that  the  force  of  torsion  is  approximately  proportional  to 
the  amount  of  twist.  In  the  case  in  point  the  upper  end  of  the  fiber 
is  turned  through  5400',  but  the  lower  end  is  turned  in  the  same 
direction  through  the  angle  h,  so  that  the  amount  of  twist  is  (5400  —  Ji). 
When  during  oscillations  the  magnet  makes  any  angle,  as  6,  with 
the  meridian  the  force  exerted  by  the  earth's  magnetism  to  pull  it 
back  into  the  meridian  is  M  H  sin  0,  and  the  force  of  torsion  acting 

,.      ,.       .     OM  H  sin  h  ,  ,. 

in  the  same  direction  is  —  ,  ,  —  and  the  resultant  of  the  two: 


,  ,  „.    .  dMHsmh      ,,„   .    .fi  6  sin  h        ~] 

MHsm  6+    5400-ft     =  MH  8ml1+sin  6  (5400  -fc)j 


since  both  h  and  6  are  small.     Hence,  in  the  oscillation  formula, 

540° 


must  be  substituted  for  M  H  in  order  to  take  into  account  the  effect 
of  torsion.  Values  of  the  logarithm  of  [5400  -r-  (5400  -  h)]  for  different 
values  of  h  are  given  in  Table  VI,  but  for  small  values  such  as  are 
usually  experienced  in  magnetometers  the  logarithm  of  this  factor 
may  be  assumed  proportional  to  h,  i.  e.  : 

log  5400  -log  (5400  -h)=7i  [log  5400  -log  (5400-  l)]  =  /t  [0.00008]. 
Induction.  —  When  a  magnet  is  placed  hi  a  magnetic  field  its  mag- 
netism is  temporarily  increased  by  induction  by  an  amount  propor- 
tional to  the  strength  of  that  component  of  the  field  which  is  parallel 
to  the  axis  of  the  magnet.  In  the  case  of  the  oscillating  magnet,  its 

/  77\ 

magnetic  moment  is  increased  from  M  to  (M+/i  H)  or  M(\+  p.  »1, 

/JL  being  the  induction  factor. 

Temperature  correction.  —  As  the  magnetic  moment  of  a  magnet 
changes  with  change  of  temperature,  increasing  as  the  temperature 
decreases  and  vice  versa,  and  as  in  general  the  temperature  of  the 
magnet  is  different  for  the  two  sets  of  observations,  deflections  and 
oscillations,  it  is  necessary  to  allow  for  this  difference  in  temperature 
before  combining  the  two  equations  to  compute  H  and  M.  If  M 


DERIVATION   OF   FORMULAS.  17 

and  M'  be  the  magnetic  moments  at  temperatures  t  and  t'  respec- 
tively, then  the  temperature  coefficient,  q,  is  represented  by  the 
formula 

Mf-  M         2 


-     t_t> 

As  (M'  —  M)  is  usually  very  small  as  compared  with  M  and  Mr  it 
will  not  introduce  a  material  error  to  substitute  either  M  or  M'  for 

—  .     The  change  in  M  with  change  in  temperature  may  then 

A 

be  computed  by  the  formula 

M'=M[l+  (t-t'}q\ 

If  t'  be  the  temperature  of  the  magnet  during  oscillations  and  t  the 
temperature  during  deflections,  then  the  formula  gives  the  magnetic 
moment  at  the  temperature  of  the  oscillations  expressed  in  terms  of 
the  moment  at  the  temperature  of  deflections. 

The  corrections  for  rate  of  chronometer  and  reduction  to  infini- 
tesimal arc  may  be  readily  applied  to  the  observed  value  of  T.  It 
is  more  convenient  to  correct  for  torsion,  induction,  and  change  of 
temperature  by  the  addition  of  three  factors  to  the  oscillation  formula 
so  that  it  becomes  : 

5400 


or 


DEFLECTIONS. 


A  magnet  free  to  turn  about  a  vertical  axis  will  come  to  rest  with 
its  magnetic  axis  in  the  magnetic  meridian  if  acted  on  by  the  earth's 
magnetism  alone.  If  a  second  magnet  be  brought  near  to  the  sus- 
pended magnet,  the  latter  will  be  deflected  out  of  the  magnetic 
meridian  by  an  amount  depending  upon  the  relative  strength  of  the 
two  forces  acting  upon  it.  The  law  of  the  action  between  two  mag- 
nets under  these  conditions  was  developed  by  Gauss  for  the  special 
cases  where  the  two  magnets  lie  in  the  same  horizontal  plane,  (1)  with 
the  axis  of  the  deflecting  magnet  in  the  magnetic  prime  vertical 
through  the  center  of  the  suspended  magnet  and  (2)  with  the  center 
of  the  deflecting  magnet  in  the  magnetic  meridian  through  the  center 
of  the  suspended  magnet  and  with  its  axis  in  the  magnetic  prime 
vertical.  Lament  later  extended  the  discussion  to  the  cases  where 
the  axes  of  the  deflecting  and  suspended  magnets  are  at  right  angles 
to  each  other,  (1)  the  deflector  being  to  the  east  or  west  and  (2)  the 
deflector  being  to  the  north  or  south.  In  1890  Borgen  developed 
the  formula  for  the  most  general  case,  placing  no  restrictions  upon 
77213—11- — 2 


18  DIRECTIONS   FOR   MAGNETIC   MEASUREMENTS. 

the  relative  positions  of  the  two  magnets,  and  derived  therefrom  the 
forms  applicable  to  the  special  cases  already  treated  by  Gauss  and 
Lamont.  Nearly  all  magnetometers  of  recent  make  are  arranged 
with  deflection  bars  attached  at  right  angles  to  the  telescope  by  which 
pointings  are  made  on  the  suspended  magnet,  and  hence  the  deflec- 
tions are  made  in  Lament's  first  posi- 
tion. It  will  be  sufficient  for  our 
purposes,  therefore,  to  outline  the 
method  of  deriving  the  deflection 
formula  for  that  special  case.  Sup- 
pose that  the  suspended  magnet 
Nj  St  is  deflected  out  of  the  magnetic 
meridian  through  the  angle  u  by  the 
magnet  N  S,  placed  so  that  the  pro- 
longation of  its  magnetic  axis  passes 
through  the  center  pf  Nt  Sr  Let  m 
^  and  m1  and  2  Z  and  2  ll  be  the  pole 
strength  and  distance  between  poles 
of  the  two  magnets  and  r  the  distance 
between  their  centers.  Then  the 
^ magnets  during  deflec-  magnetic  moments  are  H=2ml  and 

Ml  =  2mlll.  For  an  approximate  so- 
lution of  the  problem,  assume  that  Zx  is  so  small  compared  with 
r  that  the  distances  from  the  pole  N  to  .Nj  and  St  may  be  taken  as 
(r  +  Z)  and  from  S  to  Nt  and  St  as  (r  —  l).  Then  the  force  of  attrac- 

,  •          i  ,    XT     .       771  771.  .  ,    .      771  771.  Z, 

tion  between  S  and  Nj  is  -( — jL  and  the  turning  moment  is  -,      I,* 

(T  —  I)  (T  —  I) 

771  771 

The  force  of  repulsion  between  N  and  Nj  is  ,      jL  and  the  correspond- 

T 

ing  turning  moment  is   ,  _i_  yy-     The  total  turning  moment  resulting 
the  action  between  the  two  magnets  is  therefore: 

2  m  TTij  \     2m  m^  Zt  _  8  m  mlll1r  _  2  MM^  r 

-IY~~        (r2-/3)2      =(r^-Z2)2 
3  Z4     4  Z6 


The  rigorous  solution,  taking  into  account  the  pole  distance  of  N1S1 
yields  an  expression  of  the  same  form,  namely :  -  — |- 

in  which  P,  Q,  and  succeeding  coefficients  are  functions  of  the  dimen- 
sions of  the  two  magnets  and  the  distribution  of  their  magnetism. 
The  series  converges  so  rapidly  that  the  coefficients  beyond  Q  need 
not  be  considered  for  properly  chosen  deflection  distances. 

The  turning  moment  of  the  force  tending  to  pull  the  suspended 
magnet  back  into  the  meridian  is  HM1smu,  u  being  the  angle  of 


DERIVATION   OF   FORMULAS.  19 

deflection.     When  the  magnet  is  at  rest  the  two  opposing  forces  are 
equal  and  opposite, 


P  and  Q  are  called  the  first  and  second  distribution  coefficients, 
and  their  values  could  be  computed  from  the  dimensions  of  the  mag- 
nets by  means  of  Borgen's  formula,  provided  the  ratio  of  distance 
between  poles  to  length  of  magnet  was  known.  This  ratio  is  difficult 
to  determine  with  accuracy  and  appears  to  be  different  for  different 
magnets,  so  that  only  approximate  results  can  be  obtained  by  this 
method.  Borgen  concludes  that  on  the  average  the  pole  distance  is 
a  little  more  than  0.8  the  length  of  the  magnet  and,  assuming  that  it 
is  the  same  for  both  deflecting  and  suspended  magnets,  deduces  the 
formulas: 

P  =  2Z2-3Z12 


It  is  better,  in  view  of  the  uncertainty  of  the  above  ratio,  to  depend 
on  observations  for  the  determination  of  P  and  Q.  It  is  evident  that 
if  deflection  observations  are  made  at  three  distances  there  will 

TJ  • 
result  three  equations  from  which  the  three  unknowns  ^.,  P,  and  Q 

can  be  computed,  as  explained  later. 

The  above  equations  for  P  and  Q  are  useful,  however,  to  determine 
approximately  the  relative  length  of  the  two  magnets  which  will 
make  P  or  Q  zero. 

When  P  =  0     2Z2  =  3Zt2  and  Z  =  1.225^. 


When  Q  =  0    aft-lSP^+-O  and  Z  =  2.15Zr 

o 

In  deriving  the  deflection  formula  given  above  no  account  has  been 
taken  of  the  effect  of  induction  upon  the  magnetic  moment  M  of  the 
deflecting  magnet.  It  will  readily  be  seen  that  the  south  end  of  the 
deflecting  magnet  will  always  be  inclined  to  the  north  of  the  mag- 
netic prime  vertical  whether  it  is  placed  to  the  east  or  west  of  the 
suspended  magnet  or  with  its  north  end  east  or  west,  and  the  effect 
of  induction  will  therefore  always  correspond  to  a  decrease  in  its 
magnetic  moment.  As  already  stated,  the  induction  is  proportional 
to  the  strength  of  that  component  of  the  earth's  field  which  is  par- 
allel to  the  axis  of  the  magnet,  in  this  case  H  sin  u.  Hence  the 
moment  of  the  deflecting  magnet  when  the  suspended  magnet  is  de- 
flected through  the  angle  u  is  really  (M—p  H  sin  it)  instead  of  M, 
fji  being  the  induction  factor  of  the  magnet.  As  ^  H  sin  u  is  always 


20  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

very  small  in  comparison  with  M,  we  may  substitute  for  H  sin  u 
its  approximate  value  — 3- 


and  (M-f,  H  sin  u)  =    M- 


Making  this  correction  to  the  deflection  formula,  it  becomes: 
H  2 


H 
or  H- 

It  is  probable  that  the  distribution  of  the  magnetism  of  a  magnet 
changes  somewhat  in  the  course  of  time,  and  consequently  P,  Q,  and 
fi.  are  subject  to  change,  but  results  show  that  for  a  season's  work,  or 
even  longer,  they  may  be  considered  constant  without  materially 
increasing  the  uncertainty  of  the  results,  especially  when  the  magnets 
have  become  so  well  seasoned  that  the  loss  of  magnetism  is  very  slow. 
The  deflection  formula  may  then  be  written: 

H^    C 
M    sin  u 

in  which  0  =  4j  1  —  T^)(l+75  +  ^)  and  is  constant  for  a  particular 

deflection  distance  and  a  particular  temperature.  Its  variation  with 
temperature  may  be  readily  computed  from  the  coefficient  of  expan- 
sion of  the  material,  usually  brass,  of  which  the  deflection  bars  are 
made,  since  r  is  the  only  quantity  in  the  second  member  which  varies 
with  temperature. 

The  oscillations  give  the  product  of  H  and  M 


and  the  deflections  give  their  ratio: 

H_      2      A2A/       P 
M~r*  sin  u\L      iVV       f* 

from  which  the  values  of  H  and  M  can  be  readily  computed,  if  we 
assume  that  the  values  are  the  same  for  the  two  sets  of  observations. 
So  far  as  M  is  concerned  this  is  a  safe  assumption,  provided  allowance 
is  made  for  the  change  in  temperature  between  the  two  classes  of 
observations,  as  has  been  done  in  the  formula  for  H  M.  Experience 
shows  that  a  magnet  loses  its  magnetism  quite  rapidly  for  a  short  time 
after  magnetization,  but  soon  settles  down  to  a  condition  of  very  slow 
change,  inappreciable  for  the  period  covered  by  a  set  of  intensity 
observations.  Exception  should  be  made  of  the  sudden  loss  of  mag- 


DERIVATION   OF   FORMULAS.  21 

netism  resulting  from  a  shock  such  as  would  be  caused  by  dropping 
the  magnet  or  from  bringing  it  into  contact  with  another  magnet. 

In  the  case  of  H  there  is  constant  change,  usually  small  in  extent 
during  the  time  covered  by  a  set  of  observations,  but  at  times  exceed- 
ing in  amount  the  error  of  observation.  To  minimize  the  effect  of 
this  variation,  the  observations  are  usually  arranged  in  the  order: 
Oscillations,  deflections,  deflections,  oscillations.  The  following  con- 
siderations show  that  small  changes  in  H  such  as  are  exceeded  only  at 
times  of  severe  magnetic  storms  have  no  appreciable  effect  on  the 
result.  For  suppose  H0  and  Hd  are  the  values  of  H  at  the  time  of 
oscillations  and  deflections,  respectively,  and  let  Hd=H0  +  4H. 
The  combination  of  the  observations  on  the  assumption  that  H0  =  Hd 
would  give  the  value  H=^H0  Hd=^/H20  +H0  AH.  The  quantity 

under  the  radical  differs  from  (H0  +  ^JHj  by  -  —  ,  a  quantity  so 
small  as  to  be  negligible  except  in  the  case  of  a  severe  magnetic 
storm.  But  H  +  H  =  —  —  °-.  Hence  it  is  evident  that  the 


assumption  of  no  change  in  H  between  the  deflection  and  oscillation 
observations  gives  a  value  of  H  which  is  the  mean  for  the  period  cov- 
ered by  the  observations.  To  show  the  effe'ct  in  an  extreme  case, 
suppose  4H  =  Q.Q5H,  a  range  seldom  reached  in  the  course  of  a 
magnetic  storm,  then 


2  H. 


Hd+H0 
2 

Under  such  conditions  the  magnet  would  be  so  disturbed  as  to  render 
accurate  observations  impossible. 

TOTAL   INTENSITY. 

Under  certain  conditions  it  is  inconvenient  or  impossible  to  use  the 
above  method  for  determining  the  horizontal  intensity.  As  the 
magnetic  pole  is  approached  the  horizontal  intensity  becomes  so 
small  that  the  method  fails  for  lack  of  accuracy.  On  shipboard  the 
motion  of  the  vessel  precludes  the  use  of  a  fiber  suspension,  which  is 
essential  to  accurate  oscillation  observations.  At  times  it  is  neces- 
sary to  reduce  the  instrumental  equipment  of  a  party  as  much  as 
possible.  In  such  cases  use  may  be  made  of  the  method  devised  by 
Dr.  E.  Lloyd  to  determine  the  total  intensity  by  means  of  a  dip  circle. 
While  inferior  in  accuracy  under  ordinary  conditions  to  the  method  of 
determining  the  horizontal  intensity  with  a  magnetometer,  yet  with 
a  good  dip  circle  carefully  handled  it  will  usually  yield  very  satisfac- 
tory results.  (See  App.  3,  C.  &  G.  S.  Report  for  1905,  p.  114.) 

The  method  involves  two  operations,  during  both  of  which  the  dip 
circle  is  so  placed  that  the  suspended  needle  swings  in  the  magnetic 


22  DIRECTIONS   FOR   MAGNETIC   MEASUREMENTS. 

meridian:  First,  the  measure  of  the  angle  of  inclination  with  a  needle 
having  a  weight  in  the  south  end  (in  north  magnetic  latitudes)  ;  sec- 
ond, the  measure  of  the  angle  through  which  a  second  needle  is 
deflected  by  the  loaded  needle,  when  the  latter  is  placed  at  right 
angles  to  it  in  the  place  provided  for  the  purpose  between  the  reading 
microscopes,  with  the  axes  of  rotation  of  the  two  needles  lying  in  the 
same  straight  line.  In  the  first  case  the  earth's  magnetism  acting  on 
the  loaded  (intensity)  needle  is  opposed  to  the  force  of  gravity  acting 
on  the  weight.  In  the  second  case  the  force  exerted  by  the  intensity 
needle  on  the  suspended  needle  is  opposed  to  the  earth's  magnetism. 
Let  7'  =  the  dip  with  loaded  needle,  considered  positive  when  the 
south  end  is  above  the  horizon.  Then  the  angle  through  which  the 
needle  is  turned  by  the  weight  is  uf  =  1—  1' 
u  =  Deflection  angle. 

M=  Magnetic  moment  of  the  intensity  needle. 
M1  =  Magnetic  moment  of  the  second  needle. 
fc  =  Mass  of  the  weight. 

R  =  Distance  of  weight  from  the  axis  of  rotation. 
The  equation  of  equilibrium  for  the  dip  with  loaded  needle  is: 

TcR  cos  /'  =  F  M  sin  u' 
For  the  deflection  observations,  the  equation  is: 


in  which  Jct  is  a  factor  depending  upon  the  distance  between  the  needles 
and  the  distribution  of  their  magnetism.     Combining  the  two  equations  : 

WclRMMl  cos  /'  =  F2MMl  sin  u  sin  u' 
Let  Iclc.R^C2 

s 

Then  C2  cos  /'  =  F2  sin  u  sin  u' 

F=  (7Vcos  /'  esc  u  esc  u' 
G=  F^/sec  1'  sin  u  sin  u'  '. 

When  the  above  observations  are  made  at  a  place  where  the  dip 
and  horizontal  intensity  (and  hence  also  the  total  intensity)  are 
known,  the  value  of  C  can  be  computed.  Knowing  C  the  value  of 
F  at  any  other  place  can  be  determined  by  observation.  As  the 
factor  C  involves  the  mass  of  the  weight  and  its  distance  from  the 
axis  of  rotation  and  also  the  distribution  of  magnetism  in  the  needles, 
it  is  necessary  to  guard  against  change,  in  the  interval  between  the 
standardization  observations  and  those  at  other  places.  The  weight 
should  be  left  in  position  and  care  should  be  taken  not  to  change  the 
magnetic  condition  of  the  needles.  Hence  they  must  not  be  remag- 
netized  in  the  course  of  a  season's  work.  / 


DETERMINATION    OF    THE    CONSTANTS    OF    A   MAGNETOMETER.       23 
DETERMINATION  OF  THE  CONSTANTS  OF  A  MAGNETOMETER. 

The  two  formulas  used  in  the  determinatidn  of  H  and  M  from 
observations  of  oscillations  and  deflections  involve  a  number  of  factors 
which  must  be  determined  by  special  observations  or  otherwise  before 
they  can  be  used,  namely,  moment  of  inertia,  temperature  coefficient, 
induction  coefficient,  and  distribution  coefficients,  as  well  as  the 
deflection  distances. 

MOMENT    OF   INERTIA.  i 

The  magnets  of  most  magnetometers  are  of  the  collimator  type,  a 
hollow  steel  cylinder  closed  at  one  end  by  a  glass  on  which  a  scale  is 
etched  and  at  the  other  by  a  lens.  There  is  thus  introduced  a  lack 
of  homogeneity  which  makes  it  impracticable  to  compute  J£,7the 
moment  of  inertia  of  the  magnet,  from  the  dimensions  of  its  com- 
ponent parts.  Moreover  the  magnet  is  usually  supported  by  means 
of  a  stirrup  of  more  or  less  complex  form,  and  it  is  the  moment  of  the 
magnet  and  stirrup  combined  which  is  involved  in  the  formula.  It 
is  usual,  therefore,  to  determine  the  moment  of  inertia  by  means  of 
an  auxiliary  weight  of  nonmagnetic  material  and  of  regular  form  of 
which  the  moment  of  inertia  can  be  readily  computed  from  its  dimen- 
sions and  mass.  A  truly  turned  bronze  ring  or  a  circular  cylinder  of 
about  the  same  mass  as  the  magnet  are  the  forms  commonly 
employed.  For  a  ring  the  moment  of  inertia  is  given  by  the  formula: 


in  which  d  and  d±  are  the'  inner  and  outer  diameters  and  W  is  the  mass. 
For  a  cylinder  the  formula  is  : 

#i=~(4Z2  +  3<22) 

in  which  Z  is  the  length  and  d  the  diameter.  To  find  the  value  of  K^ 
for  any  other  temperature  than  the  one  at  which  the  dimensions  were 
measured,  the  average  coefficient  of  expansion  of  bronze,  0.000018 
for  1°  C.,  may  be  used,  unless  a  special  determination  has  been  made 
for  the  weight  in  question.  It  will  be  seen  that  2  log  (1.000018)  = 
0.000016  is  the  corresponding  change  in  log  Kv  for  1°  change  in  the 
temperature  of  the  inertia  weight. 

If  in  addition  to  oscillations  with  the  magnet  alone,  observations 
are  made  with  the  weight  added,  two  equations  will  result: 


Hence  K  K+ 


5400 


24  DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 

supposing  H  to  remain  constant  and  allowing  for  change  of  M  with 
change  of  temperature,  t'  being  the  temperature  of  the  magnet  dur- 
ing oscillations  without  the  weight  and  t  the  temperature  during 
oscillations  with  the  weight. 


Let       ^rgx  and 

Then  E    _K±K,  _     (T?K{ 


That  is,  this  simple  formula  may  be  used  if  the  observed  values  of  T2 
and  Jj2  are  corrected  for  torsion  and  the  former  is  reduced  to  the 
temperature  of  the,  latter.  The  following  arrangement  of  the  obser- 
vations will  practically  eliminate  small  changes  in  H: 

Begin  with  a  set  of  oscillations  without  the  inertia  weight,  deter- 
mining the  torsion  factor  with  a  torsion  weight  of  the  same  mass  as 
the  magnet.  Then  make  a  set  of  oscillations  with  the  inertia  weight 
added,  determining  the  torsion  factor  again,  but  with  a  torsion  weight 
of  the  same  mass  as  the  magnet  and  inertia  weight  combined.  Con- 
tinue making  sets  of  oscillations  alternately  with  and  without  the 
weight,  ending  the  series  with  a  set  without  the  weight.  Determine 
the  torsion  factor  again  with  the  last  set  of  each  class  of  oscillations. 
Each  set  of  oscillations  will  consist  of  8  independent  determinations 
of  the  time  of  a  selected  number  of  oscillations.  The  first  set  of 
oscillations  without  the  weight  and  the  first  half  of  the  second  set, 
combined  with  the  intervening  set  with  the  weight,  give  one  value 
of  K.  The  second  half  of  the  second  set  without  the  weight  and 
the  first  half  of  the  third  set  combined  with  the  second  set  with  the 
weight  give  another  value  of  K,  and  so  on.  Five  of  these  independ- 
ent determinations  will  usually  give  a  satisfactory  mean  value  of  K. 
The  change  in  K  with  temperature  is  a  function  of  the  temperature 
coefficient  of  steel,  which  may  be  taken  as  0.000011  for  1°  C.  For 
a  change  of  1  °  in  temperature  the  corresponding  change  in  log  K  is 

•     2  log  (1.000011)  =0.00001. 

The  method  of  separating  the  intermediate  sets  of  oscillations  with- 
out the  weight  into  two  parts  is  shown  in  the  following  example.  A 
convenient  form  of  computation  is  also  given. 


DETERMINATION    OF    THE    CONSTANTS    OF    A    MAGNETOMETER.       25 


MOMENT  OP  INERTIA.  OSCILLATIONS,  without  weight. 

Station,  Cheltenham,  Md.  Date,  April  28, 1909. 

Magnetometer  No.  26.  Magnet  26  L. 

Chronometer  No.  1107,  daily  rate  gaining  88.1  on  mean  time.  , 


Number  of 
oscillations. 

Chronometer 
time. 

Temp. 

Extreme  scale 
readings. 

Time  of  70 
oscillations. 

h.    m.     s. 

0 

15    25    15.7 

18.2 

-22.8 

+22.8 

7 

25    52.6 

14 

26    29.5 

21 

27    06.4 

28 

27    43.2 

35 

28    20.1 

42 

28    57.1 

49 

29    34.0 

18.1 

m.     s. 

70 

15    31    24.8 

6    09.1 

77 

32    01.6 

09.0 

84 

32    38.5 

09.0 

91 

33     15.3 

08.9 

98 

33    52.2 

09.0 

105 

34    29.0 

08,9 

112 

35    06.0 

08.9 

119 

35    42.9 

•    18.1 

-17.9 

+  17.9 

08.9 

Means 

18.13 

J    6    09.00    . 
i    6    08.925 

First 

Second 

half. 

half. 

s. 

s. 

t  (preceding  set)=  17.  °97 

Time  of  1           5.  27143 

5.  27036 

t—  1'=—  O.°16 

oscil. 

*  (following  set)  =  18.°27 

Corr'n  for               -49 

-49 

t-f=+0.°U 

rate                     , 

T                 5.27094 

5.  26987 

Log  T2 

1.44378 

1.44360 

"( 

'    5400    \ 

60 

60 

,5400-A/ 

«[!+(*-*')<?] 

-  5 

+  4 

"(D* 

1.  44433 

1.  44424 

(T? 

27.818 

27.812 

26 


DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 


Cheltenham,  Md. 
Magnetometer  No.  26. 


COMPUTATION  OF  MOMENT  OF  INERTIA. 


April  28, 1909. 
Inertia  ring  A. 


Chron. 
time. 

Temp. 

T2 

Ti* 
and 
2V—  T* 

Log  T* 
and 
log  Ki 

Log  T*Ki 
and 
log(7V-r*) 

log  IT 

logA'2o 

ft.  771. 

0 

14  32 

27.824 

1.  44437 

15  05 

17.97 

[27.821]            43.409          2.47036 

3.  91473 

15  29 

27.818 

15.588 

1.  19279 

2.  72194 

2.-72196 

15  32 

27.812 

1.44429 

15  52 

18.27 

[27.816] 

43.  419           2.  47036 

3.91465 

16  11 

27.820             15.603 

1.  19321 

2.  72144 

2.  72146 

16  14 

27.841                                  1.44433 

16  36 

18.53           [27.818] 

43.  416 

2.  47037 

3.  91470 

16  52 

27.794 

15.598 

1.  19307 

2.  72163          2.  72164 

16  55 

27.820 

1.44439 

17  12 

18.95           [27.822] 

43.409 

2.'  47037 

3.  91476 

17  27 

27.824 

15.587 

1.  19276 

2.72200 

2.72201 

17  30 

27.835 

1.44458 

-         , 

17  48 

19.33      |     [27.834] 

43.  433 

2.47038 

3.  91496 

18  19 

27.834 

15.599 

1.  19310 

2.72186 

2.  72187 

18  22 

27.846 

1.44476 

18  40 

20.15      !     [27.846] 

43.445 

2.  47039 

3.  91515 

19  06 

27.845 

15.599 

1.  19310 

2.  72205          2.  72205 

ftCean 

2.  72183 

JT=527.02  at  20°  C. 


When  the  weight  is  a  cylindrical  bar,  there  is  usually  a  place  pro- 
vided in  the  stirrup  for  suspending  it  above  or  below  the  magnet. 
When  a  ring  is  used,  it  must  be  balanced  on  top  of  the  magnet,  so  as 
to  be  horizontal  and  with  its  center  in  the  line  of  suspension.  To 
facilitate  placing  it  in  this  position,  a  wooden  block  is  provided  having 
a  socket  in  which  the  magnet  will  fit  with  its  upper  surface  even  with 
the  surface  of  the  block.  Suitable  marks  on  the  block  indicate  the 
position  in  which  the  ring  must  be  placed  in  order  to  be  symmetrical 
with  respect  to  the  center  of  the  magnet.  It  will,  in  general,  be  neces- 
sary to  increase  the  number  of  suspension  fibers  in  order  to  support 
the  increased  weight. 

The  moment  of  inertia  of  a  magnet  will  be  affected  by  any  change 
in  its  dimensions  or  mass.  A  screwing  up  or  unscrewing  of  one  of  the 
end  cells  would  produce  a  slight  change  of  length.  The  removal  of  a 
large  amount  of  accumulated  rust  would  produce  an  appreciable 
change  of  mass.  The  magnet  must  be  carefully  protected  therefore 
from  these  or  similar  changes,  and  in  case  such  a  change  should  take 
place  its  moment  of  inertia  must  be  redetermined. 

TEMPERATURE    COEFFICIENT. 

When  the  temperature  of  a  magnet  increases,  its  magnetic  moment 
decreases,  and  vice  versa.  Experiments  have  shown  that  the  rate  of 
change  is  not  uniform,  but  increases  with  increase  of  temperature.  In 


DETERMINATION    OF    THE    CONSTANTS    OF    A    MAGNETOMETER.        27 

view  of  the  small  change  of  temperature  usually  experienced  during 
a  set  of  horizontal  intensity  observations  and  the  partial  elimination 
of  its  effect  by  a  symmetrical  arrangement  of  oscillations  and  deflec- 
tions, no  material  error  will  be  introduced  by  the  assumption  that 
the  rate  of  change  is  uniform  for  ordinary  temperatures. 

If  M  and  Mr  be  the  values  of  the  magnetic  moment  of  a  magnet  at 
temperatures  t  and  t'  and  q  be  the  temperature  coefficient: 


M(t'-t) 

From  an  inspection  of  the  oscillation  and  deflection  formulas,  it 
will  be  seen  that  if  two  sets  of  observations  of  either  class  be  made  at 
different  temperatures,  the  value  of  q  may  be  computed,  provided 
means  are  taken  to  allow  for  change  of  H.  At  an  observatory  this 
may  readily  be  done  with  the  aid  of  the  continuous  record  of  the 
magnetograph.  In  any  case,  the  effect  may  be  nearly  eliminated  by 
observing  alternately  at  high  and  low  temperatures  and  combining 
two  sets  of  observations  at  about  the  same  temperature  with  an  inter- 
vening set  at  a  different  temperature.  Care  must  be  taken  to  main- 
tain a  given  temperature  for  a  sufficient  time  to  make  sure  that  the 
magnet  and  thermometer  are  at  the  same  temperature,  and  rapid 
changes  should  be  avoided.  If  both  oscillations  and  deflections  are 
made  at  high  and  low  temperatures,  the  change  in  H  is  obtained  from 
the  observations  themselves.  If  the  observations  are  made  in  a  room 
which  can  be  heated  and  cooled  artificially,  no  special  apparatus  is 
required.  Otherwise  the  value  of  q  is  most  conveniently  determined 
by  deflection  observations,  the  deflecting  magnet  being  surrounded 
by  a  water  jacket,  which  may  be  filled  alternately  with  hot  and  cold 
water.  In  this  case  allowance  must  be  made  for  the  effect  of  change 
of  temperature  upon  the  length  of  the  bar. 

The  computation  of  q  may  be  conveniently  made  by  logarithms, 
bearing  in  mind  that  for  our  purposes  log  (l  +  (t  —  t')g)  may  be 
replaced  by  (t  —  tf)  [log  (1  +g)]  without  materially  affecting  the  results. 

log  Mf  =  log  M+  (t-f)  log  (1  +g) 

log  Jf'-log  M 

log 


If  special  deflection  observations  have  been  made,  they  give  directly 

TT  TT 

log  M-  log  jj-,  -  log  M'  -  log  M 

H  H 

It  will  be  sufficient  to  use  the  approximate  values  of  --,,  and  -%«, 

2  2 

namely,  -5—  ^  —  and  -  --«—  .—      when  the   induction  and   distribution 

j  i  rs  sin  u  r$  sin  u 


28  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

coefficients  are  not  known,  r  and  rt  being  the  values  of  the  deflection 
distance  at  temperatures  t  and  t' . 

A  check  on  the  correctness  of  an  adopted  value  of  q  may  be  obtained 
from  the  values  of  log  M  determined  in  the  course  of  a  season's  work. 
When  all  the  values  have  been  reduced  to  a  common  temperature, 
they  should  show  a  fairly  uniform  decrease  with  lapse  of  time.  An 
error  in  the  adopted  temperature  coefficient  would  be  indicated  by 
deviations  from  a  uniform  change  which  conform  in  general  with  the 
changes  in  temperature . 

INDUCTION    COEFFICIENT. 

When  a  magnet  is  placed  in  a  magnetic  field  its  magnetic  moment 
is  temporarily  changed  by  induction  by  an  amount  which  is  propor- 
tional to  the  component  of  the  field  directed  parallel  to  the  axis  of  the 
magnet.  The  rate  of  change,  i.  e.,  the  ratio  of  the  moment  of  the 
magnet  to  the  change  produced  by  a  unit  field,  is  called  the  induction 
coefficient,  7i.  The  change  in  the  magnetic  moment  M  of  a  magnet 
placed  parallel  to  a  field  of  intensity  H  would  be  hMH,  or  fiH, 
//  =  Mh,  called  the  induction  factor,  being  the  change  in  the  magnetic 
moment  produced  by  a  field  of  unit  intensity.  The  induction  coeffi- 
cient is  not  constant,  but  varies  with  the  strength  of  magnetization  of 
the  magnet.  It  is  different  also  according  as  the  induction  tends  to 
increase  or  decrease  the  magnetic  moment;  the  more  strongly  a 
magnet  is  magnetized,  the  less  susceptible  it  becomes  to  increase  of 
magnetization  by  induction,  but  the  more  susceptible  to  decrease. 
In  the  oscillation  observations  induction  increases  the  magnetic 
moment  of  the  magnet,  and  the  induction  factor  may  be  taken  as  con- 
stant. In  the  deflection  observations  the  effect  of  induction  is  to 
reduce  the  magnetic  moment  of  the  magnet,  but  the  magnet  is  in 
general  so  nearly  in  the  prime  vertical  that  the  effect  is  very  small, 
and  hence  the  assumption  that  the  induction  factor  is  the  same  as  for 
the  oscillations  does  not  introduce  an  appreciable  error. 

Of  the  various  methods  for  determining  the  induction  coefficient, 
the  one  devised  by  Lamont  has  been  used  exclusively  by  the  Coast 
and  Geodetic  Survey.  The  magnet  of  which  the  induction  coeffi- 
cient is  desired  is  used  as  a  deflector  with  its  axis  vertical,  in  the  ver- 
tical plane  at  right  angles  to  the  suspended  magnet,  but  with  its 
center  some  distance  above  or  below  the  horizontal  plane  through  that 
magnet.  Observations  are  made  first  with  north  end  up,  magnet  up, 
and  then  with  north  end  down,  magnet  down.  In  the  former  position 
the  magnetic  moment  of  the  magnet  is  decreased  by  induction,  and  in 
the  latter  is  increased.  If  care  is  taken  to  maintain  constant  conditions , 
except  for  the  inversion  of  the  deflecting  magnet,  the  change  in  the 
deflection  angle  will  be  a  measure  of  the  change  in  the  magnetic 


DETERMINATION    OF    THE    CONSTANTS    OF    A    MAGNETOMETER.        29 

moment  due  to  the  inductive  effect  of  the  vertical  intensity,  Z.     In 
the  first  case 

H  C 


M(l—hZ) 
and  in  the  second  case 


H  _C_ 

M(l  +  hZ)     sin  u2 

\-\-JiZ     sin  u2 


+  ^i  ) 


This  method  involves  the  assumption  that  the  induction  coefficient 
is  the  same  whether  it  tends  to  increase  or  decrease  the  moment  of  the 
magnet.  As  the  corrections  for  induction  are  very  small,  this  is  a 
safe  assumption  for  all  except  the  most  refined  observations. 

As  the  induction  coefficient  is  a  very  small  quantity,  the  change  in  the 
deflection  angle  (u2  —  u^)  is  small  also  and  a  small  error  in  observa- 
tion or  a  small  change  in  the  relative  position  of  the  two  magnets  will 
materially  affect  the  result.  It  is  usual  to  extend  the  observations  by 
varying  the  position  of  the  deflecting  magnet,  as  indicated  in  the  fol- 
lowing sample  set,  and  also  by  making  several  sets  using  different 
horizontal  and  vertical  distances.  For  making  the  observations  a 
special  L-shaped  deflection  bar  is  provided,  to  which  is  pivoted  a 
vertical  arm  so  arranged  that  it  may  be  rotated  in  a  vertical  plane 
parallel  to  the  suspended  magnet,  about  a  center  in  the  horizontal 
plane  through  the  suspended  magnet. 


30 


DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 


Cheltenham,  Md. 
Magnetometer  No.  29. 
Horizontal  distance,  21  cm. 


June  16, 1905. 
Vertical  distance,  2  cm. 


No. 

Position  of  deflecting 
magnet. 

North  end. 

Horizontal  circle  readings. 

A. 

B. 

Mean. 

1 

East 

up 

up 

53  32  40 

53  32  40 

32  40 

2 

East 

down 

down 

53  56  10 

56  10 

53  56  10 

3 

East 

down 

up 

43  05  10 

05  50 

43  05  30 

4 

East 

up 

down 

43  23  40 

23  50 

43  23  45 

5 

West 

up 

down 

54  08  10 

08  10 

54  08  10 

6 

West 

down 

up 

54  28  00 

28  10 

54  28  06 

7 

West 

down 

down 

42  37  30 

37  30 

42  37  30 

8 

West 

up 

up 

13  03  00 

03  20 

43  03  10 

ft.  m. 

Time  of  beginning    9  55      Temp.         27.  2 

2  ui     East  (1-3)        10  27  10 

Time  of  ending        10  25      Temp.         27.  6 

2  tt,     West  (6-8)       11  24  55 

Mean 
i* 

2u2    East  (2-4) 

10  5G  02 
2  4400 

co  log  (#=0.20085)                                0.6971 
co  log  tan  (7=  70°  25')                          9.  5511 

10  32  25 

log  tan  J(«»-Mi) 
co  log  tan  j(uj+tti) 
log  (ft=  0.0074) 

0.  6047 
1.  0172 

2t/2    West  (5-7) 
Mean 
i«« 

11  30  40 

11  01  32 
2  45  23 

7.8701 

"  (JfiM-697)                                  2.8432 

i(uj-tti)                      0    1  23 

"  (^-5.  17)                                       0.7133 

i(ttj+ui)                      5  29  23 

DISTRIBUTION    COEFFICIENTS. 


n  the  deflection  formula 
2 


H 
~Ml 


r3  sin 


r2     r 


the  distribution  coefficients  P  and  Q  may  be  obtained  by  making 
deflections  at  three  distances  and  solving  the  three  resulting  equations 

TJ 

for  the  three  unknowns  ,  .,  P,  and  Q. 


,  ., 

.\L 


Let 


Then 


sn  H 


r    sn  u 


3  _  . 


^  (r32  - 


-  r 


*  -  r22) 


DETERMINATION    OF    THE    CONSTANTS    OF    A    MAGNETOMETER.       31 

In  case  the  relative  lengths  of  the  two  magnets  are  such  that  Q  is 
nearly  zero,  the  term   4  becomes  so  small  that  it  may  be  neglected  and 

the  value  of  P  may  be  computed  from  deflections  at  two  distances. 
Using  the  same  notation  as  above : 

S    4    X4 
Al   1+^ 

When  P  is  small  it  may  be  computed  with  sufficient  accuracy  by  the 
formula 

„   9..-   9. 

A,-\ogA2) 


For  deflection  distances  of  30  cm.  and  40  cm.  this  becomes 
P  =  4737  (log  A,- log  4,) 

It  is  evident  that  a  small  error  of  observation  in  the  deflections  will 
have  a  large  effect  on  the  accuracy  of  P,  and  little  dependence  can  be 
placed  on  the  result  from  a  single  set  of  observations.  It  is  only 
from  an  extended  series  that  a  reliable  value  of  the  distribution 

coefficients  can  be  obtained.     It  is  also  evident  from  the  form  of  the 

r  2  r  2 
factor  r  2_y  2  that  it  is  important  to  have  the  two  deflection  distances 

differ  by  a  considerable  amount.  Too  short  a  deflection  distance  is 
undesirable,  however,  since  any  uncertainty  in  the  value  of  P  has 
too  great  an  effect  on  the  resulting  horizontal  intensity,  and  too  long 
a  distance  reduces  the  size  of  the  deflection  angle  so  much  that  a 
small  error  of  observation  has  a  large  effect  on  the  result.  For  the 
size  of  magnets  generally  used,  the  distances  30  cm.  and  40  cm.  are  found 
to  be  the  most  satisfactory. 

The  above  formula  for  P  may  be  used  also  to  find  the  correction  to 
an  adopted  value  of  P  required  to  harmonize  subsequent  observa- 
tions. If  it  is  found  after  a  series  of  observations  that  the  two  values 

TT 

of  log  j^  computed  from  deflections  at  two  distances  differ  system- 
atically, one  being  greater  than  the  other  on  the  average,  the  cor- 
rection to  the  adopted  value  of  P  is  given  by  the  formula 

JP  = 


the  quantity  in  brackets  being  the  mean  value  for  the  series. 

As  already  pointed  out,  approximate  values  of  the  distribution 
coefficients  may  be  computed  from  the  dimensions  of  the  magnets. 


32  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

If  21  and  2\  be  the  pole  distances  of  the  long  and  short  magnets, 
respectively,  then 

P  =  2l2-  3ZX2  Q  =  3Z4  - 


disregarding  the  small  terms  depending  on  the  relative  diameters  of 
the  magnets.  Borgen  concluded  from  his  experiments  that  the  pole 
distance  is  on  the  average  about  0.805  the  length  of  the  magnet,  and 
this  conclusion  was  confirmed  in  part  by  the  standardization  obser- 
vations at  Kew  prior  to  1904  (Dr.  C.Chree,  "Law  of  Action  between 
Magnets."  L.,  E.,  and  D.  Phil.  Mag.,  Aug.  1,  1904).  From  the 
above  formula  it  will  be  seen  that  P  should  be  zero  when  ll\  =  1.225, 
and  this  ratio  has  been  adopted  for  the  lengths  of  the  two  magnets 
in  nearly  all  of  the  magnetometers  which  have  been  made  or  remod- 
eled by  the  Coast  and  Geodetic  Survey.  At  the  same  time  it  has 
been  the  practice  to  regard  Q  as  negligible  and  to  determine  the  value 
of  P  from  deflections  at  two  distances  in  the  manner  explained  above. 
For  seven  of  the  eight  magnetometers  to  which  the  above  ratio 
applies,  the  value  of  P  derived  in  this  way  is  in  every  case  between 
0  and  —1.0,  the  average  value  being  —0.54. 

To  show  that  this  assumption  is  justifiable,  let  us  examine  the 
results  for  five  magnetometers  of  the  design  shown  in  Figure  3, 
having  magnets  7.375  cm.  and  6.025  cm.  in  length,  i.  e.,  in  the  ratio  of 
1.224  to  1,  and  arranged  for  deflections  at  distances  of  30  cm.  and  40 
cm.  Using  Borgen'  s  ratio  of  pole  distance  to  length  of  magnet,  his 
formulas  give: 


Now  suppose  a  series  of  deflections  at  the  two  distances  gives  on  the 
average 

log  AM  -  log  A4Q  =  -  0.00020 

Assuming  Q  =  Q  P  =  4737  (log  A30-  log  ^440)  --  0.95 

which  is  about  the  upper  limit  of  the  values  found  for  this  type  of 
magnetometer.  On  the  other  hand,  if  we  assume  P  =  0,  Q  may  be 
computed  by  the  formula: 

Q  =  loge  10  -^L.  Oog  A,  -  log  A2)  =  -  546 

'2    ~~'l 

Finally,  we  may  adopt  the  value  of  Q  =  -  350  computed  from  Bor- 
gen' s  formula,  and  find  the  value  of  P  which  will  satisfy  the  equation: 


log     l+     +       ao-logl+     +       40=  -0.00020 

P        Q 

As  -a  and  4  are  both  very  small  quantities,  we  may  put 


DETERMINATION    OF    THE    CONSTANTS   OF    A    MAGNETOMETER.       33 

Hence 

=  log 


l  + 


log  (l  +  ^  30  -  log  ( 

^4o-log  (1+^)30   -0.00020  =-0.00007 
and  P  =  4737(-  0.00007)  =-0.33 

The  effect  of  the  different  values  of  P  and  Q  on  the  resulting  value 

of  H  may  be  determined  by  computing  the  value  of  log  ( 
for  the  three  cases. 


I  +     + 


P=-0.95    Q=0. 

P=0    Q=-546. 

P=-0.33    Q=-350. 

r=30cm. 

r=40cm. 

r=30cm. 

r=40cm. 

r=30cm. 

r=40cm. 

p 

r2 
Q 

7-4 

-.001056 
0 

-.000594 
0 

0 

-.000674 

0 
-.000213 

-.000367 
-.000432 

-.000206 
-.000137 

3§ 

.998944 

.999406 

.999326 

.  999787 

.999201 

.999657 

mi 

9.  99954 

9.  99974 

9.  99971 

9.  99991 

9.99965 

9.99985 

Mean 

-.00036 

-.00019 

-.00025 

It  will  be  seen  that  the  difference  between  the  logarithms  of  the 
factor  for  the  two  distances  is  in  each  case  the  assumed  difference 
between  log  A30  and  log  AM,  but  the  mean  of  the  two  is  greatest  for  the 
assumption  that  P  =  0  and  least  for  the  case  in  which  Q  =  Q.  To 
determine  the  effect  on  a  resulting  value  of  H  we  must  take  the  square 

root  offl+^  +  ^jor  divide  its  logarithm  by  two.     The  effect  of  the 

above  three  combinations  of  distribution  coefficients  would  therefore 
be  to  diminish  the  value  of  log  H  by  .00018,  .000095  and  .000125 
respectively.  The  ratio  of  the  first  two  values  is  the  number  of 
which  the  logarithm  is  .000085  or  1.0002;  that  is,  they  differ  by  only 
1  part  in  5000.  Consequently  the  error  involved  in  the  case  of  the 
Coast  and  Geodetic  Survey  magnetometers  in  assuming  that  Q  is 
negligible  does  not  amount  to  more  than  1  part  in  5000  in  H  and  is 
probably  less  than  that,  and  is  therefore  well  within  the  probable 
error  of  observation  and  reduction  in  field  work  under  favorable 
conditions. 

77213—11 3 


34  DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 

DEFLECTION    DISTANCES. 

In  a  magnetometer  with  fiber  suspension  it  is  impossible  to  avoid 
a  slight  variation  in  the  relative  positions  of  the  suspended  magnet 
and  the  deflection  bars  and  a  corresponding  variation  in  the  deflection 
distances.  To  eliminate  the  error  to  which  this  might  give  rise,  the 
instruments  are  made  either  with  two  deflection  bars,  one  on  either 
side,  or  with  a  single  bar  having  its  middle  point  over  the  center  of  the 
magnetometer.  The  deflection  observations  can  then  be  made  one- 
half  with  magnet  east  and  one-half  with  magnet  west  and  a  small 
increase  of  the  deflection  distances  on  one  side  will  be  balanced  by  a 
decrease  on  the  other  side. 

The  distance  between  corresponding  marks  on  the  two  bars  or  on  the 
two  halves  of  the  single  bar  is  twice  the  deflection  distance.  With  the 
single  straight  bar,  such  as  is  used  in  the  Kew  and  India  Survey  pat- 
tern magnetometers,  this  is  readily  obtained  by  direct  comparison  with 
a  standard  meter.  Experiments  at  Kew  have  shown  that  bars  of  this 
type  require  a  slight  correction  for  bending,  amounting  to  an  increase 
of  about  one  part  in  10000  in  the  case  of  the  instruments  of  the  latter 
type  in  use  by  the  Coast  and  Geodetic  Survey  (Fig.  4). 

In  the  Coast  and  Geodetic  Survey  pattern  magnetometer  (Fig.  3),  the 
two  bars  are  so  constructed  that  their  inner  ends  overlap  and  are  held 
together  by  two  screws.  It  is  thus  possible  to  fasten  them  together 
when  not  in  position  on  the  magnetometer  and  measure  the  deflection 
distances  as  readily  as  for  a  single  bar.  These  bars  are  very  light, 
since  the  outer  ends  are  hollow,  and  it  has  therefore  been  considered 
unnecessary  to  investigate  the  question  of  bending. 


DIRECTIONS  FOR  MAGNETIC  OBSERVATIONS  ON  LAND. 
GENERAL  DIRECTIONS. 

Selection  of  stations. — The  conditions  to  be  satisfied  in  selecting 
a  magnetic  station  are  freedom  from  present  and  probable  future  local 
disturbance,  whether  natural  or  artificial,  combined  with  convenience 
of  access.  A  station  on  suitably  situated  public  property,  or  property 
belonging  to  an  educational  institution,  is  to  be  preferred,  as  it  is  less 
likely  to  be  disturbed  or  affected  by  change  of  the  immediate  sur- 
roundings. Proximity  of  electric  railways,  masses  of  iron  or  steel, 
gas  or  water  pipes,  buildings  of  stone  or  brick  should  be  avoided. 
A  quarter  of  a  mile  from  the  first,  500  feet  from  the  second,  200 
feet  from  the  third  and  fourth  may  be  considered  safe  distances. 
The  station  should  be  at  least  50  feet  from  a  building  of  any  kind. 
If  any  doubt  arises  in  the  selection  of  a  station  as  to  the  existence  of 
local  disturbance,  two  intervisible  points  100  yards  or  more  apart 
should  be  selected  and  the  magnetic  bearing  of  the  line  joining  them 
determined  at  each  end.  A  lack  of  agreement  between  the  two 
results  would  be  evidence  of  local  disturbance.  Similar  tests  should 
then  be  made  in  other  directions  until  a  satisfactory  location  is  found. 

Description  of  station. — Each  point  occupied  should  be  described 
with  sufficient  detail  to  render  possible  its  recovery.  The  description 
should  begin  with  the  general  location  of  the  park  or  field  in  which  the 
station  is  situated.  This  should  include  the  approximate  distance 
and  direction  from  the  center  of  the  town  or  from  some  point  which 
can  be  definitely  located  on  a  map,  so  that  a  check  on  the  latitude  and 
longitude  may  be  available.  In  case  a  new  station  is  selected  in  a 
town  where  observations  had  been  made  before,  the  relative  positions 
of  the  new  and  old  stations  should  be  given,  if  possible. 

There  should  follow  measured  distances  to  the  fences  or  other  fixed 
objects  in  the  immediate  vicinity  of  the  station  and  a  description  of 
the  manner  in  which  the  station  is  marked.  If  a  meridian  line  is 
established,  the  distance  to,  and  location  of,  the  second  stone  should 
be  given,  the  magnetic  station  being  selected  so  as  to  form  one  end 
of  the  line.  It  is  desirable  also  to  give. a  rough  sketch  showing  the 
relation  of  the  station  to  surrounding  objects,  indicating  on  it  the 
direction  of  north  (which  should  always  be  toward  the  top  of  the 
sketch),  and  the  direction  of  the  marks  of  which  the  true  bearings  are 
determined. 

Marks. — These  marks  should  be  well-defined  objects  as  nearly  in 
the  horizon  as  practicable  and  likely  to  be  available  for  future  use. 

35 


36  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

It  is  desirable  to  have  the  one  selected  for  reference  fnark  in  azimuth 
and  declination  observations  in  a  souther!}"  direction,  so  that  it  may 
be  sighted  upon  through  the  opening  in  the  south  side  of  the  observing 
tent.  It  should  be  a  quarter  of  a  mile  or  more  from  the  station  if 
possible,  so  that  an  error  of  two  or  three  inches  in  reoccupying  the 
station  or  a  change  of  that  amount  in  the  position  of  the  marking 
stone  would  not  materially  affect  the  azimuth  of  the  mark.  As  an 
angle  of  1'  subtends  approximately  1  inch  at  a  distance  of  300  feet, 
the  uncertainty  at  any  given  distance  may  be  readily  computed. 

Marking  of  station. — Every  station'  sn'ould  be  marked  in  as  per- 
manent a  manner  as  conditions  will  warrant,  to  assist  in  its  subse- 
quent recovery.  Either  a  natural  or  artificial  stone,  a  glazed  drain 
pipe,  or  a  post  of  hard  wood  can  usually  be  obtained.  To  avoid  being 
disturbed,  the  station  mark  should  project  little,  if  any,  above  the 
surface  of  the  ground,  and  it  should  extend  two  feet  or  more  into 
the  ground. 

Meridian  line. — When  a  meridian  line  is  to  be  established  the 
azimuth  observations  must  be  made  with  especial  care  and  the  com- 
putations revised  before  the  stones  are  set.  The  line  should  be  not 
less  than  300  feet  long  (if  possible  not  less  than  500  feet),  and  extra 
precautions  should  be  taken  to  secure  the  marking  stones  against 
future  disturbance. 

Repeat  stations. — Where  observations  are  to  be  made  at  an  old 
station  for  the  purpose  of  determining  the  secular  variation,  especial 
effort  should  be  made  to  reoccupy  the  precise  point  at  which  the 
earlier  observations  were  made.  Any  changes  in  the  immediate  sur- 
roundings should  be  noted  in  the  description  of  station.  If  local 
conditions  have  changed  to  such  an  extent  that  a  reoccupation  is 
clearly  undesirable,  then  a  new  station  must  be  established.  There 
may  be  cases,  however,  in  which  it  will  be  best  to  reoccupy  the  old 
station  and  also  establish  a  new  one;  e.  g.,  the  old  station,  while  not 
satisfying  the  requirements  of  future  availability,  may  still  suffice  to 
determine  the  secular  variation  since  the  former  observations.  When, 
owing  to  change  in  the  immediate  surroundings  or  defect  of  the 
original  description,  it  is  impossible  to  locate  the  exact  point  from 
the  measured  distances,  the  desired  result  may  sometimes  be  accom- 
plished with  the  aid  of  the  bearings  of  prominent  objects.  Having 
three  well-defined  objects  which  were  connected  by  angular  measures 
at  the  time  of  the  former  occupation,  successive  trials  with  the  the- 
odolite will  serve  to  locate  the  spot  at  which  those  angular  measures 
are  reproduced. 

Care  of  instruments. — Care  should  be  taken  to  keep  the  instruments 
in  good  adjustment  and  free  from  dust.  The  magnets  should  be 
touched  with  the  hands  as  little  as  possible  and  should  always  be 
wiped  dr}r  with  clean  chamois  or  soft  tissue  paper  at  the  close  of 


GENEBAL  DIRECTIONS.  37 

observations  to  prevent  them  from  rusting.  They  must  not  be 
dropped  or  allowed  to  touch  each  other  or  other  iron  or  steel  objects. 
They  should  be  kept  in  the  instrument  box  with  north  end  down, 
packed  snugly  to  avoid  jars  in  transportation.  The  dip  needles 
should  be  wiped  with  tissue  paper  both  before  and  after  observations 
and  the  pivots  cleaned  with  pith.  In  reversing  polarities,  the  bar 
magnets  should  be  drawn  smoothly  from  center  to  ends  of  the  needle, 
as  nearly  parallel  to  the  axis  of  the  needle  as  possible.  In  case  the 
needle  projects  above  the  surface  of  the  reversing  block  the  magnets 
must  not  bear  heavily  upon  it. 

Chronometer. — The  utmost  care  must  be  exercised  in  carrying  the 
chronometer.  A  pocket  chronometer  requires  more  careful  handling 
than  a  watch  to  secure  a  constant  rate.  It  must  be  kept  at  as  uniform 
a  temperature  as  possible  and  wound  at  the  same  hour  each  day.  It 
must  be  protected  from  jarring  or  shaking.  Past  experience  indi- 
cates that  the  best  results  are  obtained  when  it  is  carried  in  the 
trousers  watch  pocket.  Where  unusual  rough  travel  is  anticipated 
it  is  well  to  compare  the  chronometer  with  a  well-regulated  watch 
both  before  and  after  the  journey.  At  least  once  a  week,  and  at 
every  station  if  possible  without  serious  delay,  the  chronometer 
correction  on  standard  time  should  be  obtained  by  means  of  Western 
Union  or  other  telegraphic  time  signals.  The  chronometer  correction 
and  rate  are  given  the  sign  with  which  they  must  be  applied.  For  a 
chronometer  which  is  fast  and  gaining  they  are  both  negative. 

Order  of  observations. — When  a  complete  instrumental  outfit  is 
supplied  the  observations  at  a  station  comprise:  Morning  and  after- 
noon azimuth,  latitude  at  noon;  one  set  of  dip  with  each  of  two 
needles;  two  sets  each  of  declination,  oscillations,  and  deflections; 
angular  measures  between  prominent  objects.  It  is  desirable  that 
the  azimuth  observations  should  be  made  at  nearly  equal  times 
(preferably  not  less  than  two  hours)  before  and  after  apparent  noon, 
giving  nearly  the  same  altitude  of  the  sun  for  the  morning  and  after- 
noon sets.  The  effect  on  the  azimuth  of  a  small  error  in  latitude 
is  in  that  way  eliminated.  Latitude  observations  should  extend  not 
more  than  15  minutes  before  or  after  apparent  noon  (maximum 
altitude  of  the  sun). 

As  the  declination  and  horizontal  intensity  are  usually  changing 
more  rapidly  in  the  morning  than  in  the  afternoon,  it  is  preferable 
to  make  the  magnetometer  observations  in  the  afternoon.  They 
should  be  made  in  the  order:  Declination,  oscillations,  deflections, 
deflections,  oscillations,  declination.  The  second  set  of  deflections 
and  oscillations  should  be  made  with  magnets  inverted,  and  the 
horizontal  circle  should  be  shifted  in  azimuth  before  the  second  set 
of  declination,  in  order  to  bring  the  readings  upon  a  different  part 
of  the  circle. 


38  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

Thermometer. — The  same  thermometer  should  be  used  throughout 
a  set  of  horizontal  intensity  observations.  It  should  be  placed  in 
the  hole  in  the  magnet  house  during  oscillations  and  near  to  the 
deflecting  magnet  during  deflections,  either  in  the  end  of  the  deflec- 
tion bar  or  (in  magnetometers  of  the  India  Survey  pattern)  in  the 
box  in  which  the  magnet  is  inclosed.  It  should  be  changed  from 
one  bar  to  the  other  with  the  magnet.  Care  must  be  taken  to  stop 
up  the  hole  in  the  magnet  house  when  the  thermometer  is  not  in  it. 
Before  beginning  observations  the  thermometer  should  be  examined 
to  see  that  the  mercury  column  is  not  broken  and  that  none  of  the 
mercury  is  in  the  upper  recess.  A  broken  column  can  usually  be 
joined  by  holding  the  thermometer  in  the  hand  and  striking  the 
wrist  sharply  against  the  knee,  or  by  attaching  it  securely  to  a  string 
and  swinging  it  rapidly  in  a  circle. 

Agreement  of  results. — Before  leaving  a  station  the  computation 
should  be  carried  far  enough  to  showr  that  there  is  nothing  essentially 
wrong  with  the  observations.  In  good  work  two  consecutive  sets  of 
azimuth  should  agree  within  one  minute  and  the  morning  and  after- 
noon sets  within  two  minutes.  A  greater  difference  is  usually  due 
to  lack  of  adjustment  or  level  of  the  theodolite,  or  to  a  mistake  in 
pointing  on  the  wrong  limb  of  the  sun,  or  in  using  the  wrong  line  of 
,  the  diaphragm.  In  case  the  morning  and  afternoon  azimuth  obser- 
vations give  results  differing  by  more  than  five  minutes,  the  observa- 
tions should  be  repeated.  The  two  sets  of  declination  should  agree 
within  two  or  three  minutes  when  corrected  approximately  for 
diurnal  variation  (see  Table  IX).  The  values  of  log  Mil  for  the 
two  sets  of  oscillations  should  not  differ  by  more  than  0.00100,  and 

TT 

the  values  of  log  ,,  should  agree  equally  well.     The  corresponding 

agreement  to  be  expected  in  the  values  of  T  and  u  can  easily  be  com- 
puted for  a  particular  magnetometer  and  a  particular  locality. 

When  the  dip  results  for  the  two  needles  differ  by  more  than  five 
minutes  in  excess  of  the  normal  difference  of  the  needles,  the  observa- 
tions should  be  repeated.  Thus,,  if  the  observations  show  that  on 
the  average  needle  No.  1  gives  a  value  of  dip  three  minutes  greater 
than  No.  2,  the  observations  should  be  repeated  when  No.  1  gives  a 
result  more  than  eight  minutes  greater  or  two  minutes  less  than 
No.  2. 

The  record  should  be  kept  with  hard  pencil  (or  fountain  pen)  and 
entered  at  once  on  the  proper  form  (not  kept  on  blank  paper  and 
afterwards  copied  onto  the  form.)  All  computations  should  be  made 
in  ink  or  inked  over  before  the  record  is  sent  to  the  Office.  The 
different  sheets  will  be  punched  and  fastened  together  in  the  covers 
provided  (Form  367),  arranged  in  the  following  order:  (1)  Descrip- 
tion of  station,  angles  connecting  the  azimuth  mark  with  other 


EQUIPMENT.  39 

prominent  objects,  and  chronometer  correction  on  Standard  time 
(Form  441),  (2)  latitude  observations  (Form  267),  (3)  azimuth 
observations  (Form  266),  (4)  azimuth  computation  (Form  269), 
(5)  declination  (Form  37),  (6)  dip  (Form  42),  (7)  oscillations  (Form 
41),  (8)  deflections  (Form  39). 

Abstract. — Before  the  record  is  sent  to  the  Office  the  computation 
should  be  completed  and  a  copy  made  of  the  results  and  also  of  such 
quantities  as  would  be  required  to  replace  the  computation  in  case 
the  record  is  lost  (Form  442).  This  includes  brief  description  of 
station,  chronometer  corrections  on  Standard  time,  sun's  maximum 
altitude  from  latitude  observations;  mean  of  chronometer,  horizontal 
and  vertical  circle  readings  for  each  set  of  azimuth;  mean  reading  of 
mark  and  magnet,  mean  scale  reading  erect  and  inverted  for  each 
declination  set;  time  of  whole  number  of  oscillations  and  effect  of 
90°  torsion,  mean  value  of  2u  for  each  deflection  distance,  tempera- 
ture and  time  of  each  set  of  observations;  the  mean  dip  with  each 
needle  for  each  half  set  (before  and  after  reversal  of  polarities). 

Computations.— Five-place  logarithms  will  be  used.  In  the  azi- 
muth observations  the  means  of  circle  readings  will  be  carried  to 
whole  seconds,  means  of  times  to  tenths  of  a  second;  similarly  in 
computations.  For  declination  observations,  carry  mean  scale  read- 
ings to  hundredths  of  a  division,  balance  of  computation  to  tenths  of 
a  minute.  For  oscillations,  compute  time  of  one  oscillation  to  four 
decimal  places,  mean  temperature  to  tenths  of  a  degree.  Compute 
deflection  angles  to  whole  seconds.  Dip  computations  will  be  carried 
to  tenths  of  a  minute. 

To  secure  the  best  results,  particular  attention  should  be  paid  to 
the  following  points : 

Be  sure  that  all  articles  of  iron  and  steel  are  removed  to  a  safe  distance 
before  beginning  magnetic  observations. 

Be  sure  that  the  instrument  is  level  and  the  levels  in  adjustment  before 
beginning  observations,  especially  in  latitude  and  azimuth  observations. 

Be  careful  to  keep  the  magnets  and  dip  needles  dry  and  clean,  espe- 
cially the  pivots  of  the  dip  needles. 

Handle  the  chronometer  with  care  at  all  times. 

EQUIPMENT. 

Observers  engaged  exclusively  on  magnetic  work  are  usually  pro- 
vided with  a  theodolite  magnetometer,  a  dip  circle,  a  half-second 
pocket  chronometer,  a  tent,  and  minor  accessories.  When  magnetic 
observations  are  to  be  made  only  as  opportunity  offers  in  connection 
with  other  branches  of  the  field  work  of  the  Survey,  the  equipment 
is  often  less  complete,  either  a  dip  circle  with  special  needles  for  total 
intensity  observations  and  a  compass  attachment  for  determination 
of  the  magnetic  declination  or  simply  a  compass  declinometer  for 


40  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

declination  alone.  In  such  cases  the  true  meridian  is  usually  known 
from  triangulation  or  else  the  instrumental  equipment  includes  a 
theodolite  and  timepiece  with  which  the  necessary  astronomical 
observations  can  be  made. 

In  the  descriptions  of  instruments  and  methods  which  follow,  the 

erm  alidade  will  be  used  to  designate  the  upper  part  of  the  instru- 

ment to  which  are  attached  the  verniers  for  reading  the  horizontal 

circle  and  of  which  the  motion  is  controlled  by  the  upper  clamp  and 

tangent  screw. 

LATITUDE  FROM  OBSERVATIONS  OF  THE  SUN. 

For  the  greater  part  of  the  United  States  only  approximate  values 
of  the  latitude  and  longitude  can  be  obtained  from  existing  maps. 
It  is  usual,  therefore,  to  include  latitude  observations  in  the  program 
of  work  at  a  magnetic  station,  in  order  that  the  azimuth  may  be 
determined  from  sun  observations  with  the  required  accuracy. 
The  most  convenient  method  involves  the  measurement  of  the  sun's 
altitude  at  or  near  apparent  noon,  using  the  small  theodolite  pro- 
vided for  the  azimuth  observations. 

At  apparent  noon,  when  the  sun  is  on  the  meridian 


0  being  the  latitude  of  the  place,  £  the  sun's  zenith  distance,  and 
d  its  declination,  south  zenith  distance  and  north  declination  being 
considered  positive  for  the  northern  hemisphere.  As  the  sun's  decli- 
nation changes  so  slowly  (the  hourly  rate  of  change  never  amounts 
to  1'),  no  appreciable  error  is  introduced  by  assuming  it  constant  for 
a  series  of  observations  beginning  a  few  minutes  before  noon  and 
ending  a  few  minutes  after  noon.  The  maximum  altitude  may  also 
be  taken  as  the  meridian  altitude.  The  observations  are  made  in  the 
manner  shown  in  the  example  given  below. 

The  observations  should  begin  about  ten  minutes  before  apparent 
noon  and  end  about  ten  minutes  after  noon.  Before  making  the 
observations,  therefore,  it  is  necessary  to  find  the  chronometer  time 
of  apparent  noon,  at  least  approximately,  by  the  method  given  below. 
After  setting  up,  leveling,  and  adjusting  the  theodolite,  as  explained 
later  in  connection  with  azimuth  observations,  the  method  of  observ- 
ing is  as  follows  : 


LATITUDE   FROM   OBSEKVATIONS   OF   THE   SUN. 
Form  267. 

OBSERVATIONS  or  SUN  FOR  LATITUDE. 


41 


Station,  Smyrna  Mills,  Me. 
Theodolite  of  mag'r  No.  20. 
Chronometer  No.  245. 


Date,  Friday,  August  5, 1910. 
Observer,  H.  E.  McComb. 
Temperature,  24°  C. 


Sun's 
limb. 

V.C. 

Chronometer 
time. 

Vertical  circle. 

A. 

B. 

Mean. 

h.  m.  s. 

0        ,        „ 

/    // 

•    /    it 

U 

R 

11  30  04 

61  14  00 

13  30 

61  13  45 

L 

L 

11  31  16 

119  23  00 

20  00 

60  38  30 

L 

L 

11  33  14 

119  22  30 

19  30 

60  39  00 

U 

R 

11  34  38 

61  16  30 

15  30 

61  16  00 

U 

R 

11  36  36 

61  17  00 

15  30 

61  16  15 

L 

L 

11  37  34 

119  21  30 

19  00 

60  39  45 

L 

L 

11  39  32 

119  21  30 

19  00 

60  39  45 

U 

R 

11  40  33 

61  17  30 

16  00 

61  16  45 

U 

R 

11  42  46 

61  16  30 

15  00 

61  15  45 

L 

L 

11  43  30 

119  22  30 

2000 

60  38  45 

Obs'd  max.  alt. 

6058  15 

R.  &P. 

—  27 

h 

60  57  48 

r 

29  02  12 

8 

17  06  18 

4 

46  08  30 

With  the  vertical  circle  to  the  right  of  the  telescope,  point  on  the 
sun  with  its  disc  bisected  by  the  vertical  line  of  the  diaphragm  and  its 
upper  limb  tangent  to  the  horizontal  line.  Record  the  time  of  con- 
tact as  indicated  by  the  chronometer  and  read  and  record  both 
verniers,  A  and  B,  of  the  vertical  circle.  Turn  the  alidade  180°  in 
azimuth  and  make  another  pointing  on  the  sun,  but  with  its  lower 
limb  tangent  to  the  horizontal  line  of  the  diaphragm,  again  recording 
the  time  and  vertical  circle  reading.  As  the  vertical  circle  is  usually 
graduated  from  0°  to  360°,  the  reading  in  the  first  case  will  be  the  alti- 
tude of  the  sun's  upper  limb,  but  the  second  reading  must  be  subtracted 
from  180°  to  get  the  altitude  of  the  sun's  lower  limb.  Combining  the 
two  gives  the  altitude  of  the  sun's  center  and  eliminates  the  vertical 
collimation  error  of  the  theodolite  and  the  index  error  of  the  graduation. 
The  observations  are  continued  for  15  or  20  minutes,  reversing  the 
circle  after  the  odd  pointings,  as  shown  in  the  above  example.  The 
level  of  the  instrument  should  be  examined  after  the  even  pointings 
and  corrected  if  necessary.  If  the  beginning  is  properly  timed,  the 
maximum  altitude  will  occur  near  the  middle  of  the  series.  For  the 
field  computation  the  pair  of  readings  is  selected  which  gives  the 
maximum  altitude,  and  their  mean,  after  being  corrected  for  refraction 
and  parallax  (Table  I),  is  combined  with  the  sun's  declination  to  get 
the  latitude.  The  quantities  for  vertical  circle  left  in  the  column 


42 


DIRECTIONS   FOR   MAGNETIC   MEASUREMENTS. 


headed  "Mean"  are  really  180°  minus  the  means  of  the  two  vernier 
readings. 

A  more  accurate  value  of  latitude  is  obtained  by  utilizing  all  the 
observations  by  the  "method  of  circum-meridian  altitudes/'  ex- 
plained in  detail  in  most  textbooks  on  spherical  astronomy  (see,  for 
example,  Chauvenet,  Vol.  I,  page  235).  In  view  of  the  degree  of 
accuracy  required  in  a  magnetic  survey,  or  possible  with  the  small 
theodolite  ordinarily  used,  many  approximations  in  the  method  of 
reduction  to  the  meridian  may  be  made.  If  Ji  be  the  sun's  meridian 
altitude,  7i0  its  altitude  (observed)  at  a  time  t  before  (or  after)  appar- 
ent noon,  then  approximately: 

,      ,  2  sin2  M 

h  =  h0  +  cos  (f>  cos  d  esc  £        —= ,", 

SllJ.   J. 


2  sin2  bt 
Let  A  =  cos  (/>  cos  d  esc  £  and    m  =  —  — ^rr 

Then  Ji  =  h0-\-  Am  and  <f>  =  d  -\-  r 

% 

Table  III  gives  the  values  of  m  for  different  values  of  t  and  Table  IV 
gives  the  values  of  A  for  different  values  of  </>  and  d.  It  will  be  seen 
that  A  increases  as  the  sun's  zenith  distance  decreases,  and  the  method 
is  therefore  not  well  adapted  for  observations  where  the  sun  crosses 
the  meridian  near  the  zenith.  The  following  computation  of  the  set 
of  observations  given  above  will  best  illustrate  the  method. 

Form  268. 

COMPUTATION  OF  LATITUDE  FROM  CIRCUM-MERIDIAN  ALTITUDES  OF  SUN. 


Station,  Smyrna  Mills,  Me. 


Date,  August  5, 1910. 


h.  m.  a. 

Chron.  correction  on  L.  M.  T.       +  27  20 

Local  mean  time  of  app.  noon       12  05  53 
Chron.  time  of  apparent  noon       11  38  33 

t 

m 

A 

A  m 

Reduced  h  of 
sun's  limb. 

0         /       // 

61  16  57 
60  40  51 

Reduced  h 
of0 

m.  8. 

-8  29 
-7  17 

141 
104 

1.36 

192 
141 

0          1       II 

60  58  54 

-5  19 

56 

76 

60  40  16 

-3  55 

30 

41 

61  16  41 

-1  57 

8 

11 

61  16  26 

-0  59 

2 

3 

60  39  48 

+0  59 
+200 

2 

8 

3 

11 

60  39  48 
61  16  56 

60  58  22 

+4  13 
+4  57 

35 

48 

48 
65 

61  16  33 
60  39  50 

60  58  12 

Mean 

60  58  25 

R.  &P. 

-  27 

h 

60  57  58 

C 

290202 

9 

17  06  19 

* 

46  08  21 

LATITUDE  FROM  OBSERVATIONS  OF  THE  SUN.         43 

In  order  to  obtain  the  values  of  t,  the  time  of  observation  before  or 
after  apparent  noon,  it  is  necessary  to  find  the  chronometer  time  of 
apparent  noon.  The  chronometer  correction  on  local  mean  time  is 
usually  obtained  from  the  observations  of  the  sun  for  azimuth  and 
time,  as  will  be  seen  later,  but  it  may  be  obtained  also  from  an  approx- 
imate value  of  the  longitude  and  the  chronometer  correction  on 
standard  time,  as  follows:  For  Smyrna  Mills,  Me.,  suppose  the  ap- 
proximate longitude,  68°  08'. 5,  or  4h  32m  34s,  to  be  obtained  from  a 
map.  By  comparison  with  Western  Union  telegraphic  time  signals  on 
August  4,  1910,  chronometer  No.  245  was  6s. 0  fast  on  75th  meridian 
mean  time.  On  August  5  it  was  5s. 8  fast,  showing  a  loss  of  0s. 2  per 
day. 

m.    s. 

At  noon  August  5  chronometer  No.  245  correction  on  75th  mer.  m.  t —6 

Smyrna  Mills  east  of  75th  meridian 27  26 

Therefore  chronometer  No.  245  correction  on  local  mean  time +27  20 

To  find  the  local  mean  time  of  apparent  noon,  we  must  know  the 
difference  between  mean  time  and  apparent  time;  that  is,  the  equa- 
tion of  time,  E.  This  may  be  found  in  any  ephemeris.  On  page  128 
of  the  American  Ephemeris  for  1910,  the  value  of  E  at  Greenwich 
apparent  noon  on  August  5  is  found  to  be  5m  53s. 7  and  decreasing  at 
the  rate  of  0s. 23  per  hour.  Hence,  for  Smyrna  Mills  apparent  noon, 
which  occurs  4h  32m  later,  the  value  of  E  would  be  5m  538.7-  ls.0  = 
5m  52s. 7.  This  is  the  amount  which  must  be  added  to  apparent  time 
in  order  to  obtain  mean  time.  As  the  equation  of  time  for  apparent 
noon  never  differs  from  the  equation  of  time  for  mean  noon  by  as 
much  as  0s. 2,  the  latter  may  be  used  when  the  sun's  ephemeris  for 
apparent  noon  is  not  available.  The  apparent  time  of  apparent 
noon  is  always  12h  00m  00s,  hence  the  mean  time  of  apparent  noon  at 
Smyrna  Mills  on  August  5,  1910,  was  12h  05m  53s.  The  chronometer 
was  found  to  be  27m  20s  slow  of  local  mean  time.  Hence  the  chro- 
nometer time  of  apparent  noon  was  1 1 h  38m  33s.  Expressed  analytically : 
Chronometer  time  of  apparent  noon  =  mean  time  of  apparent  noon  — 
chronometer  correction,  bearing  in  mind  that  the  correction  is  con- 
sidered positive  when  the  chronometer  is  slow  and  negative  when  it 
is  fast.  By  subtracting  the  chronometer  time  of  apparent  noon 
from  the  chronometer  time  of  each  observation,  the  corresponding 
value  of  t  is  found.  This  is  the  argument  required  for  obtaining  m 
from  Table  III. 

For  obtaining  the  values  of  A  from  Table  IV  only  approximate 
values  of  cf>  and  d  are  required,  but  as  the  value  of  d  is  needed  later  it 
is  just  as  well  to  compute  it  at  this  point. 

h.    m.   s. 

Chronometer  time  of  apparent  noon 11  38  33 

Chronometer  correction  on  75th  meridian  mean  time -  06 

75th  meridian  time  slow  on  Greenwich  mean  time. . .  +5  00  00 


Greenwich  mean  time  of  local  apparent  noon 4  38  27 


44  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

This  is  the  Greenwich  mean  time  for  which  the  sun's  declination  is 
required.  By  referring  to  page  129  of  the  American  Ephemeris  for 
1910  it  will  be  found  that  the  sun's  declination  at  Greenwich  mean 
noon  on  August  5  was  17°  09'  25".  8  N.,  and  decreasing  at  the  rate  of 
40/M9  per  hour.  This  rate  is  not  uniform,  however,  the  value  for 
noon  of  the  6th  being  40  ".88.  As  the  declination  at  4h  38m  278,  or 
4h.64  after  noon  is  required,  we  must  find  the  average  hourly  change 
for  that  interval,  or,  what  is  approximately  the  same  thing,  the  change 
for  the  middle  of  the  interval,  or  2h.32  after  noon.  As  the  hourly 
change  increased  0".69  in  24  hours,  it  increased  about  TV  of  of  that 
amount,  or  0".07  in  2.3  hours,  and  the  desired  average  value  for  the 
interval  is  therefore  40".19  +  0".07  =  40".26. 

Sun's  declination  at  Greenwich  mean  noon  Aug.  5  ...................  17  09  25.8  N  . 

Change  for  4h.64=4.64X40".26=186".8  .......  ......................       -3  06.8 

Sun's  declination  at  4h  38m  27§  after  noon  .................  '-/.?v  .......  17  06  19.  0  I*  . 

In  practice  it  is  sufficient  to  carry  the  hourly  change  to  tenths  of 
seconds  only,  and  the  allowance  for  second  differences  may  then  be 
made  by  inspection.  In  fact,  in  most  cases  second  differences  might 
be  neglected  entirely,  as  the  maximum  error  would  be  only  3  ".5  in 
assuming  that  the  tabular  value  of  hourly  change  is  uniform  for  12 
hours  before  and  12  hours  after  the  noon  to  which  it  refers. 

The  product  Am  is  the  difference  between  the  altitude  of  the  sun 
at  noon  and  at  the  time  t  before  or  after  noon,  and  must  therefore  be 
added  to  the  observed  altitude  in  order  to  get  the  corresponding 
meridian  altitude.  The  altitude  of  the  sun's  center  is  found  by  com- 
bining an  altitude  ol  the  upper  limb  with  one  of  the  lower  limb.  The 
mean  of  the  different  results  is  treated  as  the  maximum  altitude  was 
in  the  approximate  field  computation. 

LATITUDE  FROM  OBSERVATIONS  OF  POLARIS. 

If  desired  the  latitude  may  be  readily  determined  by  observing  the 
altitude  of  the  pole  star,  when  the  longitude  and  local  mean  time  are 
known  approximately,  using  the  formula: 

(j)  =  h  —  p  cos  t  +  ^P2  sin2  t  sin  1"  tan  Ji 

£i 

t  being  the  hour-angle  of  the  star,  p  its  polar  distance,  and  Ji  the  ob- 
served altitude  corrected  for  refraction.  The  refraction  may  be 
obtained  from  Table  I  if  the  tabular  quantities  are  increased  by 
8".  8  cos  h,  the  amount  of  the  solar  parallax.  When  observations  are 
made  at  upper  or  lower  culmination,  the  formula  becomes 


The  right  ascension  and  declination  of  Polaris  for  each  day  of  the  year 
are  given  in  the  American  Ephemeris.     There  also  will  be  found  on  the 


DETERMINATION   OF   THE   TRUE   MERIDIAN.  45 

last  page  of  the  book  a  table  giving  the  altitude  of  the  star  above  or 
below  the  pole  at  any  hour-angle,  computed  for  latitude  45°  and  the 
mean  declination  of  the  star  for  the  year. 

DETERMINATION  OF  THE  TRUE  MERIDIAN  AND  LOCAL  MEAN  TIME  BY 
MEANS  OF  OBSERVATIONS  OF  THE  SUN. 

The  following  method  is  the  one  usually  employed  to  determine 
the  true  meridian  in  connection  with  the  magnetic  observations  of 
the  Coast  and  Geodetic  Survey.  It  is  more  convenient  than  others 
in  that  it  may  be  employed  during  daylight  when  the  magnetic 
observations  are  in  progress.  In  connection  with  the  time  signals  sent 
out  by  telegraph  from  astronomical  observatories  it  furnishes  the 
means  also  of  determining  approximately  the  longitude  of  the  place  of 
observation.  It  requires  a  theodolite  with  a  vertical  circle  and  pris- 
matic eyepiece  for  observing  the  sun,  and  a  well-regulated  time- 
piece. The  observations  at  a  place  usually  consist  of  four  independent 
sets  of  observations,  two  in  the  morning  and  two  in  the  afternoon, 
each  set  comprising  four  pointings  on  the  sun  and  two  pointings  on  a 
reference  mark,  symmetrically  arranged  as  in  the  example  given 
below.  For  each  pointing  on  the  sun  the  time  is  noted,  and  the 
horizontal  and  vertical  circles  are  both  read.  For  the  best  results 
the  observations  sliould  be  made  not  less  than  two  hours  from 
apparent  noon. 

ADJUSTMENT   OF   THE    THEODOLITE. 

Before  beginning  observations  it  is  necessary  to  see  that  the  theod- 
olite is  in  good  adjustment,  especially  as  regards  the  levels. 

To  adjust  the  levels. — After  mounting  the  theodolite  on  the  tripod, 
set  up  the  instrument  over  the  station  mark  with  the  tripod  head 
approximately  level  and  the  legs  planted  firmly  in  the  ground  or 
resting  on  suitable  stubs.  Most  small  theodolites  are  provided  with 
a  quick  centering  device,  by  means  of  which  the  accurate  setting 
over  the  station  mark  is  made  after  the  tripod  has  been  fixed  in 
position.  Turn  the  alidade  until  one  of  the  levels  is  parallel  to  the 
line  joining  two  of  the  leveling  screws.  Bring  the  level  bubble  to  the 
center  of  the  vial  by  means  of  the  leveling  screws.  Bring  the  bubble 
of  the  second  level  to  the  center  of  its  vial  by  means  of  the  third 
leveling  screw  (by  the  other  pair  of  leveling  screws,  if  there  are  four). 
If  necessary,  repeat  the  operation  until  both  bubbles  are  in  the 
center.  Then  turn  the  alidade  180°  in  azimuth.  If  the  levels  are 
out  of  adjustment,  the  bubbles  will  no  longer  be  in  the  center  of  the 
vials.  Correct  one  half  of  the  defect  by  means  of  the  adjusting 
screws  of  the  levels  and  the  other  half  by  means  of  the  leveling  screws. 
Return  the  alidade  to  its  original  position  and  repeat  the  operation 
if  necessary.  When  the  adjustment  has  been  completed  the  instru- 
ment will  be  level  and  the  level  bubbles  will  be  in  the  center  of  the 
vials  no  matter  in  what  direction  the  telescope  is  pointing. 


46  DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 

To  insert  new  cross  wires. — The  cross  wires  of  a  telescope  are  at- 
tached to  a  metal  ring  which  is  held  in  position  near  the  eyepiece 
by  four  capstan  screws.  They  may  be  spider  threads  (obtained  from 
a  cocoon,  not  from  a  web),  or  fine  platinum  wire,  or,  more  commonly, 
lines  etched  on  a  thin  piece  of  glass,  called  a  diaphragm,  which  is 
fastened  to  the  ring  by  shellac.  An  extra  diaphragm  and  a  small 
bottle  of  shellac  should  be  kept  with  the  instrument  so  that  the 
observer  may  insert  a  new  diaphragm  should  he  be  so  unfortunate  as 
to  break  the  old  one.  To  do  this  the  eyepiece  is  removed,  the  ring 
taken  out,  and  the  remains  of  the  old  diaphragm  and  shellac  cleaned 
off.  The  ring  is  then  laid  on  a  piece  of  white  paper  and  the  new 
diaphragm  placed  in  the  position  indicated  by  lines  on  the  ring  and 
fastened  by  shellac  around  the  edges.  The  ring  is  then  put  back  in 
the  telescope  tube,  and  adjusted  in  position  by  means  of  the  capstan 
screws  as  explained  later. 

To  adjust  the  eyepiece. — Point  the  telescope  to  the  sky  and  move 
the  eyepiece  in  or  out  until  the  cross  wires  appear  sharp  and  distinct. 
Then  turn  the  telescope  to  a  distant  object  and  move  the  object  glass 
in  or  out  until  the  object  appears  sharply  defined.  If  the  adjust- 
ment has  been  properly  made  there  will  be  no  apparent  motion  of 
the  object  when  the  eye  is  moved  from  one  side  of  the  eyepiece  to 
the  other.  If  the  vertical  cross  wire  is  perpendicular  to  the  hori- 
zontal axis  of  the  theodolite,  an  object  which  has  been  bisected  by 
one  part  of  the  wire  will  continue  to  be  bisected  throughout  the 
length  of  the  wire  when  the  telescope  is  revolved  about  its  horizontal 
axis.  If  this  is  not  the  case  the  capstan  screws  should  be  loosened 
and  the  ring  carrying  the  cross  wires  rotated  slightly  about  the 
optical  axis.  In  the  field  the  verticality  of  this  cross  wire  may  be 
tested  by  pointing  on  the  vertical  edge  of  a  house.  At  the  same  time 
the  horizontality  of  the  transverse  axis  of  the  telescope  may  be  tested 
by  turning  the  telescope  in  altitude  and  seeing  whether  the  edge  of 
the  house  remains  bisected  for  a  considerable  change  in  altitude. 

To  adjust  the  vertical  cross  wire  for  collimation. — Point  at  a  well- 
defined  distant  object.  Turn  the  alidade  180°  in  azimuth  and  reverse 
the  telescope  and  point  on  the  object  again.  The  amount  by  which 
the  difference  of  the  two  circle  readings  differs  from  180°  is  twice  the 
error  of  collimation  and  may  be  corrected  by  moving  laterally  the 
ring  carrying  the  cross  wires,  by  means  of  the  capstan  screws  on  the 
sides  of  the  telescope  tube.  When  the  telescope  is  mounted  eccen- 
trically, as  it  is  in  some  magnetometers,  allowance  must  be  made  for 
that  fact  in  adjusting  for  collimation.  Two  marks  must  be  provided 
which  are  twice  as  far  from  each  other  as  the  optical  axis  of  the  tele- 
scope is  from  the  vertical  axis  of  the  instrument. 

This  adjustment  is  usually  attended  to  by  the  mechanician  before 
the  instrument  is  sent  from  the  office  and  rarely  needs  to  be  repeated 
in  the  field  unless  it  becomes  necessary  to  insert  new  cross  wires,  since 


DETERMINATION   OF   THE   TRUE   MERIDIAN.  47 

the  observations  are  so  arranged  as  to  eliminate  small  errors  of  col- 
limation. 

To  adjust  the  vertical  circle  to  redd  zero  when  the  telescope  is  level.— 
While  the  observations  are  usually  so  arranged  as  to  eliminate  the 
effect  of  index  error  of  the  vertical  circle  and  vertical  collimation 
error  of  the  telescope,  it  is  desirable  to  keep  that  error  small  so  that 
a  setting  on  the  wrong  limb  of  the  sun  or  an  error  in  reading  the 
circle  may  be  more  readily  discovered.  This  adjustment  is  made  by 
means  of  a  slow-motion  screw  which  operates  on  an  arm  of  the  frame 
carrying  the  verniers  by  which  the  vertical  circle  is  read.  Bisect  a 
distant  object  with  the  horizontal  cross  wire  and  read  the  vertical 
circle.  Turn  the  alidade  180°  in  azimuth,  invert  the  telescope,  and 
again  point  on  the  object  and  read  the  vertical  circle.  If  the  sum  of 
the  two  readings  differs  from  180°,  correct  for  half  the  difference  by 
means  of  the  slow-motion  screw  which  moves  the  verniers.  When 
this  adjustment  has  been  made,  the  level  attached  to  the  vernier 
frame  may  be  adjusted  also.  In  some  theodolites  the  vertical  circle 
is  not  attached  rigidly  to  the  telescope,  but  is  held  by  friction  or  by 
a  clamp.  In  making  the  above  adjustment  for  an  instrument  of 
that  class,  a  first  approximation  is  obtained  by  shifting  the  position 
of  the  graduated  circle,  and  then  the  process  is  completed  by  moving 
the  verniers. 

OBSERVATIONS. 

Having  leveled  and  adjusted  the  theodolite  and  selected  a  suitable 
azimuth  mark,  a  well-defined  object  nearly  in  the  horizon  and  more 
than  100  yards  distant,  the  azimuth  observations,  are  made  in  the 
following  order,  as  shown  in  the  sample  set  given  below. 

Point  on  the  mark  with  vertical  circle  to  the  right  of  the  telescope 
(V.  C.  R.)  and  read  the  horizontal  circle,  verniers  A  and  B.  Reverse 
the  circle,  invert  the  telescope  and  point  on  the  mark  again,  this 
time  with  vertical  circle  left  (V.  C.  L.).  Place  the  colored  glass  in 
position  on  the  eyepiece  and  point  on  the  sun  with  vertical  circle 
left,  bringing  the  horizontal  and  vertical  cross  wires  tangent  to  the 
sun's  disc.  At  the  moment  when  both  cross  wires  are  tangent  note 
the  time  by  the  chronometer.  If  an  appreciable  interval  is  required 
to  look  from  the  eyepiece  to  the  face  of  the  chronometer,  the  observer 
should  count  the  half-seconds  which  elapse  and  deduct  the  amount 
from  the  actual  chronometer  reading.  The  horizontal  and  vertical 
circles  are  then  read  and  recorded.  A  second  pointing  on  the  sun 
follows,  using  the  same  limbs  as  before.  The  alidade  is  then  turned 
180°  and  the  telescope  inverted  and  two  more  pointings  are  made, 
but  with  the  cross  wires  tangent  to  the  limbs  of  the  sun  opposite  to 
those  used  before  reversal.  This  completes  a  set  of  observations. 
A  second  set  usually  follows  immediately,  but  with  the  order  of  the 
pointings  reversed,  ending  up  with  two  pointings  on  the  mark. 
Between  the  two  sets  the  instrument  should  be  releveled  if  necessary. 


48 


DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 


To  avoid  the  necessity  of  moving  both  tangent  screws  hi  making  a 
setting  on  the  sun,  it  is  convenient  to  clamp  the  circles  with  one 
cross  wire  slightly  in  advance  of  the  limb  and  then  wait  until  the 
limb  moves  up  to  it,  at  the  same  time  keeping  the  other  cross  wire 
tangent  by  means  of  the  tangent  screw.  As  the  wires  are  seen  more 
distinctly  when  brightly  illuminated,  the  limbs  to  be  observed  should 
be  so  selected  that  one  wire  may  cross  the  sun's  disc  until  the  moment 
of  tangency  is  reached.  The  observer  must  be  sure  to  point  on 
opposite  limbs  in  the  two  halves  of  a  set,  so  that  the  mean  of  the 
four  readings  will  refer  to  the  sun's  center.  If  he  should  make  the 
mistake  of  pointing  on  the  wrong  limb,  the  reading  must  be  corrected 
for  the  sun's  diameter.  For  a  vertical  circle  reading  the  correction 
is  the  diameter,  which  may  be  obtained  from  an  ephemeris  of  the 
sun  or  with  sufficient  accuracy  from  the  second  column  of  Table  II. 
For  a  horizontal  circle  reading,  the  sun's  diameter  must  be  divided 
by  the  cosine  of  the  sun's  altitude  in  order  to  get  the  desired  cor- 
rection. The  values  for  altitudes  from  10°  to  70°  are  given  in 
Table  II. 


Form  266. 


OBSERVATIONS  OP  SUN  FOR  AZIMUTH  AND  TIME. 


Station,  Smyrna,  Mills,  Me. 
Theodolite  of  mag'r  No.  20. 
Mark,  Flagpole  on  school  bulldinp. 
Chronometer,  245. 


Date,  Friday,  August  5,  1910. 
Observer,  H.  E.  McComb. 
Temperature,  20°  C. 


Sun's 
limb. 

V.  C. 

Chronome- 
ter time. 

Horizontal  circle.            Vertical  circle. 

A. 

B.     Mean.      A. 

8.     Mean. 

L 

Mark 

124  43  40 

43  50   124  43  45 

R 

' 

304  43  40 

43  40   304  43  40 

124  43  42 

h.  m.  s. 

El 

R 

8  25  54 

155  12  30 

12  50   155  12  40    41  10  30 

11  30   41  11  00 

El 

R 

27  56     155  40  40 

41  00   155  40  50    41  31  00 

31  30   41  31  15 

Q 

L       30  03     337  00  10 

00  20   337  00  15   138  47  00 

45  30   41  13  45 

D 

L 

32  06 

337  28  20 

28  30 

337  28  25   138  27  00 

2.5  30   41  33  45 

8  28  59.8 

336  20  32 

41  22  20 

—  57 

JQ      L     8  33  45     337  51  00 

51  20 

337  51  10   138  10  30   09  00   41  50  15 

IQ 

L       35  59     338  24  30 

24  50 

338  24  40   137  48  30   47  00   42  12  15 

( 

R       38  20     158  10  00   10  20 

158  10  10    43  10  30   11  30   43  11  00 

El 

R       40  37     158  41  50   42  10 

158  42  00    43  31  30   32  30   43  32  00 

8  37  10.2 

338  17  00                  42  41  23 

—  54 

R     Mark       304  43  40   43  50 

304  43  45 

L               124  43  20   43  40   124  43  30 

124  43  38 

DETERMINATION   OF   THE   TRUE   MERIDIAN. 


49 


Form  266. 


OBSERVATIONS  OP  SUN  FOR  AZIMUTH  AND  TIME. 


Station,  Smyrna  Mills,  Me. 
Theodolite  of  mag'r  No.  20. 
Mark,  Flagpole  on  school  building. 
Chronometer,  245. 


Date,  Friday,  August  5, 1910. 
Observer,  H.  E.  McComb. 
Temperature,  21°  C. 


Sun's 
limb. 

v.  c 

Chronome- 
ter time. 

Horizontal  circle. 

Vertical  circle. 

A. 

B. 

Mean. 

A. 

B. 

Mean. 

0             /       // 

/     // 

Off/ 

0         /          // 

/     // 

•     in 

R 

Mark 

28045  00 

45  20 

280  45  10 

L 

100  45  20 

45  40 

100  4530 

280  45  20 

ft.  m.  s. 

d 

L 

3  12  38 

96  35  50 

36  20 

96  36  05 

143  03  00 

00  00 

36  58  30 

El 

L 

14  38              97  01  20 

01  50 

97  01  35 

143  23  00 

2000 

36  38  30 

® 

R 

16  44            278  04  10 

04  30 

278  04  20 

36  53  30 

53  00 

3653  15 

® 

R 

18  46 

278  29  00 

2920 

278  29  10 

36  33  00 

32  00 

36  32  30 

3  15  41.  5 

277  32  48 

3645  41 

. 

—    1  08 

.0 

R 

3  20  12 

278  47  20 

47  40 

278  47  30  !      36  18  00 

1730 

36  1745 

B 

R 

22  12 

279  12  00 

12  20 

279  12  10  i      35  58  00 

57  30 

35  5746 

^ 

L 

23  50 

98  57  40 

58  10 

98  57  55 

144  56  30 

53  30 

35  05  00 

0 

L 

25  50 

99  22  40 

23  10 

99  2255 

145  17  00 

1400 

34  4430 

3  23  01.0 

279  05  08 

35  31  15 

—  1  11 

L 

Mark 

100  45  20 

45  40 

100  45  30 

R 

280  45  20 

45  30 

280  45  25 

28045  28 

The  chronometer  and  circle  readings  for  the  four  pointings  of  a  set 
are  combined  to  get  mean  values  for  the  subsequent  computation. 
When  the  vertical  circle  is  graduated  from  zero  to  360 °,  the  readings 
with  vertical  circle  right  give  the  apparent  altitude  of  one  limb  of  the 
sun,  while  those  with  vertical  circle  left  must  be  subtracted  from  180° 
to  get  the  apparent  altitude  of  the  other  limb.  The  mean  of  the  four 
pointings  gives  the  apparent  altitude  of  the  sun's  center.  This  must 
be  corrected  for  refraction  and  parallax  to  get  the  true  altitude. 
The  value  of  this  correction  is  given  in  Table  I  for  different  tem- 
peratures and  altitudes  for  average  conditions.  The  change  in  refrac- 
tion with  change  in  barometric  pressure  need  not  be  taken  into  con- 
sideration. The  correction  for  refraction  is  so  large  and  uncertain 
near  the  horizon  that  observations  of  the  sun  should  be  avoided  when 
its  altitude  is  less  than  10°. 

It  is  important  to  test  the  accuracy  of  the  observations  as  soon  as 
they  have  been  completed,  so  that  additional  sets  may  be  made  if 

77213—11 4 


50  DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 

necessary.  This  may  be  done  by  comparing  the  mean  of  the  first  and 
fourth  pointings  of  a  set  with  the  mean  of  the  second  and  third,  or  by 
comparing  the  rate  of  change  in  the  altitude  and  azimuth  of  the  sun 
between  the  first  and  second  pointings,  the  third  and  fourth,  fourth 
and  fifth,  fifth  and  sixth,  and  seventh  and  eighth.  For  the  period 
of  15  or  20  minutes  required  for  two  sets  of  observations  the  rate  of 
motion  of  the  sun  does  not  change  much. 

COMPUTATION. 

For  the  computation  of  the  azimuth  of  the  sun  and  the  local  mean 
time  from  observations  made  in  the  above  manner,  use  is  made  of  the 
following  formulas,  the  derivation  of  which  has  been  explained  in 
the  first  part  of  this  publication. 


ctn2  %A  =  sec  s  sec  («  —  p)  sin  (s  —  h)  sin  (s  —  <j>) 
tan  %t  =  sin  (a  —  h)  sec  (s  —  p)  tan 


A  =  azimuth  of  sun,  east  of  south  in  the  morning,  west  of  south  in 
the  afternoon. 

<j>  =  latitude  of  the  place. 

h  =  altitude  of  the  sun  corrected  for  refraction  and  parallax. 

p  =  polar  distance  of  the  sun  at  the  tune  of  observation. 


£  =  the  hour  angle  of  the  sun,  or  apparent  time  of  observation, 
expressed  in  arc. 

The  form  of  computation  is  shown  in  the  following  example,  for  the 
sets  of  observations  at  Smyrna  Mills,  Me.,  given  above. 


DETERMINATION   OF  THE   TRUE   MERIDIAN. 


51 


Form  269. 

COMPUTATION  OF  AZIMUTH  AND  LONGITUDE. 

Station,  Smyrna  Mills,  Me. 


Date. 

Aug.  5. 

Aug.  5. 

Aug.  5. 

Aug.  5. 

h 

41    21    29 

42    40    29 

36    44    33 

35    30    04 

* 

46    08    21 

46    08    21 

46    08    21 

46    08    21 

P 

72    51    34 

72    51    39 

72    56    08 

72    56    12 

2s 

160    21    24 

161    40    29 

155    49    02 

154    34    37 

s 

80    10    42 

80    50    14 

77    54    31 

77    17    18 

s-p 

7    19    08 

7    58    35 

4    58    23 

4    21    06 

s-h 

38    49    13 

38    09    45 

41    09    58 

41    47    14 

s-t 

34    02    21 

34    41    53 

31    46    10 

31    08    57 

log  sec  * 

0.  76807 

0.  79795 

0.  67887 

0.  65749 

"  sec  (s—p) 

0.00355 

0.00422 

0.00164 

0.00125 

11  sin  (s-h) 

9.  79718 

9.  79091 

9.81839 

9.82371 

"  sin  («-tf) 

9.74800 

9.75530 

9.  72140 

9.71372 

"  ctn«M 

0.31680 

0.34838 

0.22030 

0.  19617 

"  ctnM 

0.15840 

0.  17419 

0.  11015 

0.09808 

A  from  South 

69    33    04 

67    36    43 

75    37    17 

77    10    09 

Circle  reads 

336    20    32 

338    17    00 

277    32    48 

279    05    08 

S.  Mer.    " 

45    53    36 

45    53    43 

201    55    31 

201    54    59 

Mark       " 

124    43    42 

124    43    38 

280    45    20 

280    45    28 

Azimuth  of  Mark 

78    50    06 

78    49    55 

78    49    49 

78    50    29 

Mean 

78    50    05 

log  sec  (s—p)  sin  (s—  h) 

9.80073 

9.  79513 

9.82003 

9.82496 

"  tan  \  t 

9.  64233 

9.  62094 

9.70988 

9.72688 

t  in  arc 

47    23    24 

45    20    52 

54    17    25 

56    07    55 

h.  m.      s. 

h.   m.      s. 

ft.    TO.        S. 

ft.    TO.     *. 

t 

-3    09    33.6 

-3    01    23.5 

3    37    09.7 

3  44   31.7 

E 

+        5    53.4 

+        5    53.3 

+        5    51.8 

+       5   51.8 

Local  M.  T. 

8    56    19.8 

9    04    29.8 

3    43    01.5 

3   50   23.5 

Chron.  time 

8    28    59.8 

8    37    10.  2 

3    15    41.5 

3   23   01.0 

A  t  on  L.  M.  T. 

+      27    20.0 

+      27    19.6 

+      27    20.0 

+     27  22.5 

J  t  on  75  M.  T. 

5.8 

5.8 

5.8 

5.8 

41 

-27    25.8 

-27    25.4 

-27    25.8 

—27    28.3 

Mean 

-27    26.3= 

-  6°  51'.6 

A=68° 

08'.4 

The  different  steps  of  the  computation  are  most  conveniently  made 
in  the  following  order: 

Enter  the  corrected  altitude,  mean  readings  of  the  horizontal  circle 
for  the  pointings  on  the  sun  and  on  the  mark,  and  the  chronometer 
time  for  each  set  of  observations  in  their  proper  places.  Enter  the 
value  of  latitude  obtained  from  the  latitude  observations  or  other 
source.  Compute  the  chronometer  correction  on  standard  time  for 
the  time  of  each  set  of  observations  from  the  comparisons  with 


52  DIRECTIONS  FOE  MAGNETIC   MEASUREMENTS. 

telegraphic  time  signals.  Unless  the  chronometer  has  a  large  rate 
its  correction  may  be  taken  the  same  for  two  contiguous  sets  of 
observations.  Compute  the  Greenwich  mean  time  of  observation  for 
each  set,  and  find  from  the  American  Ephemeris,  or  H.  O.  Publication 
No.  118,  the  sun's  polar  distance  and  the  equation  of  time  for  that 
time  in  the  manner  explained  in  connection  with  the  computation  of 
latitude  from  circum-meridian  altitudes.  The  succeeding  steps 
require  little  explanation.  As  the  horizontal  circles  of  theodolites 
are  with  few  exceptions  graduated  clockwise,  and  as  the  sun  is  east 
of  south  in  the  morning  and  west  of  south  in  the  afternoon,  it  follows 
that  in  order  to  find  the  horizontal  circle  reading  of  the  south  point, 
the  azimuth  of  the  sun  must  be  added  to  the  circle  reading  of  the  sun 
for  the  morning  observations  and  subtracted  from  it  for  the  after- 
noon observations.  The  horizontal  circle  reading  of  the  south  point 
subtracted  from  the  mark  reading  gives  the  azimuth  of  the  mark, 
counted  from  south  around  by  west  from  0  to  360°. 

For  the  computation  of  t,  the  logarithms  of  sec  (s  —  p)  and  sin  (s  —  h) 
are  found  in  the  azimuth  computation  and  their  sum  can  be  written 
down  in  its  proper  place.  From  that  must  be  subtracted  log  ctn  £  A 
to  find  log  tan  %t.  The  corresponding  value  of  t  is  the  time  before  or 
after  apparent  noon.  If  in  the  case  of  the  morning  observations 
ctn  i^  be  substituted  for  tan  ty,  ^  will  be  counted  from  midnight. 
The  difference  between  the  chronometer  correction  on  local  mean 
time  and  the  correction  on  standard  time  is  the  difference  in  longi- 
tude between  the  standard  meridian  and  the  place  of  observation. 

The  angular  measures  connecting  selected  prominent  objects  are 
conveniently  made  in  connection  with  the  mark  readings  at  the 
close  of  the  azimuth  observations.  The  various  marks  should  be 
pointed  on  successively  with  vertical  circle  left  and  then  in  the 
reverse  order  with  vertical  circle  right.  They  should  be  well-defined 
objects  not  liable  to  be  confused  with  similar  ones  near  by.  The  edge 
of  a  chimney,  for  example,  is  not  a  desirable  mark,  as  there  is  always 
danger  of  confusing  the  edges  as  they  appear  to  the  naked  eye  with 
their  reversed  position  as  seen  through  the  telescope. 

DETERMINATION  OF  THE  TRUE   MERIDIAN  FROM  OBSERVATIONS  OF 

POLARIS. 

The  true  meridian  may  also  be  determined  by  measuring  the  angle 
between  Polaris  and  a  reference  mark,  when  the  local  mean  time  is 
known.  The  most  convenient  time  for  observing  is  just  after  sunset, 
when  the  mark  does  not  require  illumination.  The  azimuth  of  the 
star  from  the  north  is  computed  by  means  of  the  formula 

—  sin  t 
tan  A  = 


cos  $  tan  d  —  sin  cf>  cos  t 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION.  53 

in  which  t  is  the  hour  angle  of  the  star  before  or  after  upper  culmina- 
tion and  d  is  its  declination.  For  the  purposes  of  magnetic  work  it  is 
sufficient  to  know  the  local  mean  time  within  one  or  two  minutes. 
At  elongation  the  change  in  the  azimuth  of  Polaris  is  inappreciable 
for  a  considerable  interval  and  even  a  less  accurate  knowledge  of  the 
time  will  suffice.  When  the  local  time  is  not  known  the  time  of 
culmination  of  Polaris  may  be  determined  with  sufficient  accuracy 
from  a  knowledge  of  its  position  with  relation  to  £  Ursse  Majoris  or 
8  Cassiopeia. 

A  detailed  explanation  of  these  methods  of  determining  the  true 
meridian,  together  with  tables  to  facilitate  their  use,  will  be  found  in 
"  Principal  Facts  of  the  Earth's  Magnetism,"  pages  79-91. 

DETERMINATION  OF  THE  MAGNETIC  DECLINATION. 
A.    WITH  A  MAGNETOMETER. 

The  determination  of  the  magnetic  declination  consists  of  two 
operations ;  first,  the  determination  of  the  true  meridian  as  explained 
in  the  preceding  section,  and  second  the  determination  of  the  mag- 
netic meridian,  using  either  a  magnetometer,  a  compass  declinometer, 
or  the  compass  attachment  of  a  dip  circle. 

Coast  and  Geodetic  Survey  pattern  magnetometer. — Most  of  the  mag- 
netometers in  use  in  the  field  work  of  the  Coast  and  Geodetic  Survey 
are  similar  in  design  to  the  one  shown  in  Figure  3.  It  is  usually  re- 
ferred  to  as  a  theodolite  magnetometer  since  it  comprises  a  theodolite 
and  a  magnetometer  arranged  for  mounting  on  the  same  base.  It  is 
light,  compact,  of  simple  construction,  and  easily  handled  and  is 
therefore  especially  suited  to  the  field  work  of  a  magnetic  survey. 
The  horizontal  circle  is  5  inches  in  diameter  graduated  to  20'  and 
read  by  two  verniers  to  20".  The  magnets  are  hollow,  octagonal, 
1.1  cm.  between  opposite  faces.  The  lengths  of  the  two  magnets 
(7.4  and  6.0  cm.)  are  such  as  to  make  the  first  distribution  coefficient 
(P)  nearly  zero.  The  observer  faces  south  when  making  observa- 
tions of  the  suspended  magnet.  In  the  south  end  of  each  magnet  is 
a  graduated  scale  and  in  the  north  end  a  collimating  lens  so  arranged 
that  when  the  reading  telescope  is  focused  on  a  distant  object  the 
graduated  scale  will  be  in  focus  also.  The  magnet  is  supported  in  a 
brass  stirrup  consisting  of  three  parallel  connected  rings  joined  to  a 
shank  about  2.5  cm.  long.  This  long  shank  presents  any  appreciable 
change  of  level  of  the  magnet  for  a  considerable  change  of  vertical 
force.  A  short  pin  in  the  center  of  the  stirrup  engages  a  groove  about 
the  center  of  the  magnet.  With  the  octagonal  form  of  magnet  the 
scale  is  easily  placed  horizontal  in  either  the  erect  or  inverted  posi- 
tions. When  not  in  use  the  stirrup  is  attached  to  a  hook  under  the 
roof  of  the  magnet  house  to  prevent  breaking  or  twisting  of  the  fiber. 


54 


DIRECTIONS  FOB   MAGNETIC    MEASUREMENTS. 


Silk  fiber  suspension  is  used,  two  strands  usually  being  sufficient  to 
support  the  magnets  without  danger  of  breaking.  The  upper  ends 
of  the  fibers  are  held  by  a  clamp,  with  a  suitable  arrangement  of  screw 
and  nut  or  rack  and  pinion  for  regulating  the  height  of  the  suspended 
magnet. 


FIG.  3.— Coast  and  Geodetic  Survey  pattern  magnetometer. 

The  end  of  the  reading  telescope  is  connected  with  one  end  of  the 
wooden  magnet  house  by  a  hood  of  dark  cloth,  so  that  no  glass  comes 
between  the  objective  and  the  magnet.  Light  to  illuminate  the  scale 
of  the  magnet  is  admitted  through  a  hole  in  the  other  end  of  the 
magnet  house.  This  hole  is  closed  by  a  glass  window,  which  is 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION.  55 

opened  when  pointings  are  to  be  made  on  the  mark  in  declination 
observations,  in  order  to  avoid  the  distortion  likely  to  be  caused  by 
irregular  refraction  of  the  glass. 

The  deflection  bars  used  in  the  horizontal  intensity  observations 
are  of  such  shape  that  the  deflecting  magnet  when  in  position  on  the 
bar  is  on  a  level  with  the  optical  axis  of  the  reading  telescope  and  at 
right  angles  with  it  and  consequently  with  the  suspended  magnet 
also.  The  bars  are  not  graduated,  but  on  each  there  are  two  troughs 
for  supporting  the  deflecting  magnet.  In  the  middle  of  each  trough 
is  a  short  pin  which  fits  into  the  groove  around  the  magnet  and  thus 
insures  its  proper  setting.  The  pins  are  approximately  30  and  40  cm. 
from  the  center  of  the  magnet  house.  In  Figure  3  the  long  magnet 
is  in  position  on  the  deflection  bar,  and  the  wooden  sides  of  the  magnet 
house  have  been  removed  to  show  the  suspended  short  magnet. 
The  theodolite  shown  at  the  right  of  the  picture  is  easily  mounted  in 
place  of  the  magnetometer  when  azimuth  or  latitude  observations 
are  to  be  made. 

In  order  to  minimize  the  change  in  torsion  with  change  in  atmos- 
pheric conditions,  the  silk  fibers  should  be  well  soaked  in  glycerin 
before  they  are  used.  Extra  fibers  should  be  kept  in  soak  in  a  bottle 
of  glycerin,  to  be  ready  for  use  in  case  of  breakage.  A  convenient 
way  to  insert  new  fibers  is  as  follows:  Draw  the  fibers  through  the 
fingers  several  times  to  remove  superfluous  glycerin  and  undesirable 
twists.  Fasten  one  end  to  the  eye  of  the  stirrup  with  a  small  loop. 
Draw  the  fibers  even  and  fasten  a  small  piece  of  wax  or  other  weight 
to  the  loose  ends.  Eemove  the  torsion  head  from  the  suspension 
tube,  turn  the  magnet  house  upside  down,  and  drop  the  weighted  ends 
through  the  tube.  The  wax  may  then  be  removed  and  the  ends 
fastened  to  the  torsion  head  at  the  proper  distance  from  the  stirrup, 
care  being  taken  to  have  the  two  fibers  of  the  same  length.  When 
the  torsion  head  is  at  its  lowest  position  the  stirrup  should  be  about 
half  an  inch  above  the  floor  of  the  magnet  house.  Especial  care  must 
be  taken  to  leave  no  loose  ends  which  might  touch  the  magnet  house 
or  the  inside  of  the  suspension  tube. 

The  determination  of  the  magnetic  meridian  with  this  type  of 
magnetometer  is  made  as  follows:  Mount  the  magnetometer  and 
level  carefully  by  means  of  the  striding  level  provided  for  the  reading 
telescope  (shown  in  position  in  the  picture).  Turn  the  alidade  until 
the  telescope  points  approximately  magnetic  south.  Place  the 
thermometer  in  the  hole  in  the  roof  of  the  magnet  house,  suspend  the 
torsion  weight  (a  solid  brass  cylinder  of  about  the  same  mass  as  the 
long  magnet),  and  replace  the  wooden  sides  of  the  magnet  house  by 
those  of  glass.  Bring  the  torsion  weight  to  rest  and  then  watch  its 
vibration  under  the  influence  of  the  twist  of  the  suspension  fibers. 
By  successive  trials  turn  the  torsion  head  at  the  top  of  the  suspension 


56  DIRECTIONS  FOE  MAGNETIC   MEASUREMENTS. 

tube  until  the  weight  comes  to  rest  in  a -position  parallel  to  the  optical 
axis  of  the  telescope,  or  until  its  arc  of  vibration,  reduced  to  a  small 
amount,  is  bisected  by  that  line.  The  suspension  is  then  free  from 
twist — that  is,  there  is  no  tendency  to  turn  a  suspended  weight  out  of 
the  vertical  plane  through  the  optical  axis  of  the  telescope — and  the 
reading  of  the  torsion  head  indicates  the  line  of  detorsion.  With  a 
silk  fiber  suspension  just  strong  enough  to  support  the  magnet,  the 
effect  of  90°  of  torsion  seldom  amounts  to  as  much  as  5'  and  an  error 
of  10°  in  the  determination  of  the  line  of  detorsion  would  therefore 
affect  the  resulting  decimation  by  not  more  than  0'.5. 

Open  the  glass  window  in  the  end  of  the  magnet  house  and  point 
upon  the  object  used  as  a  reference  mark  in  the  azimuth  observa- 
tions, lowering  the  torsion  weight  below  the  line  of  sight.  Read  both 
verniers  and  enter  the  readings  in  the  proper  place  in  the  record. 

Close  the  window,  turn  the  alidade  until  the  telescope  again  points 
approximately  magnetic  south,  remove  the  torsion  weight  and  sus- 
pend in  its  place  the  long  magnet  with  its  scale  erect,  being  careful 
to  slacken  the  fibers  as  little  as  possible.  Raise  the  magnet  to  the 
level  of  the  reading  telescope,  quiet  its  vibration  as  much  as  possible, 
and  replace  the  wooden  sides  of  the  magnet  house.  Adjust  the 
mirror  so  that  it  reflects  the  light  onto  the  scale  of  the  magnet. 

Check  the  vibration  of  the  magnet  until  the  arc  is  reduced  to  one 
or  two  divisions  of  the  scale.  This  may  be  done  by  means  of  a  screw- 
driver, adjusting  pin,  or  other  small  piece  of  steel,  holding  it  a  short 
distance  from  the  end  of  the  magnet,  first  on  one  side  and  then  on 
the  other  as  the  magnet  swings  back  and  forth.  It  will  often  be 
found  that  an  adjusting  pin  has  become  slightly  magnetized.  In 
such  cases  the  alternate  attraction  and  repulsion  may  be  produced 
by  turning  the  pin  end  for  end. 

Turn  the  alidade  until  the  division  of  the  scale  corresponding  to  the 
magnetic  axis  swings  by  about  equal  amounts  to  the  right  and  left 
of  the  vertical  wire  of  the  reading  telescope,  and  clamp  the  hori- 
zontal circle.  If  the  scale  reading  of  the  axis  is  not  known  approxi- 
mately from  previous  observation,  the  middle  division  of  the  scale 
will  be  used.  This  setting  of  the  horizontal  circle  is  not  to  be  changed 
until  the  time  comes  to  point  on  the  mark  again. 

Read  the  scale  when  the  magnet  comes  to  rest  momentarily  at  the 
extremes  of  its  swing.  When  the  scale  is  not  numbered  it  is  assumed 
to  be  erect  when  the  longer  divisions  project  upward  and  the  readings 
are  then  considered  as  increasing  from  left  to  right.  The  "left" 
reading  is  the  one  when  the  left  end  of  the  scale  approaches  nearest 
to  the  vertical  wire  of  the  reading  telescope,  and  is  therefore  less 
than  the  "right"  reading  for  magnet  erect.  After  an  interval  of  a 
minute  read  the  scale  again. 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION. 


57 


Turn  the  magnet  upside  down  in  the  stirrup,  so  that  the  scale  ap- 
pears inverted,  reduce  the  arc  of  vibration,  and  make  four  readings 
of  the  scale  at  intervals  of  one  minute.  The  zero  of  the  scale  is  now 
to  the  right,  and  the  "left"  reading  will  be  greater  than  the  " right. " 

Return  the  magnet  to  the  erect  position  and  make  two  more 
scale  readings. 

Read  the  horizontal  circle  to  be  sure  that  it  has  not  been  disturbed 
accidently;  remove  the  magnet  and  complete  the  set  by  pointing  on 
the  reference  mark.  When  horizontal  intensity  observations  are 
to  follow  immediately,  as  is  usually  the  case,  it  is  more  convenient 
to  make  the  first  set  of  oscillations  before  removing  the  magnet  and 
repeating  the  pointing  on  the  mark. 

The  mean  of  the  erect  and  inverted  readings  gives  the  division  of 
the  scale  which  corresponds  to  the  position  of  the  magnetic  axis. 
When  the  telescope  is  pointed  on  that  division,  it  is  in  the  plane  of  the 
magnetic  meridian.  For  any  other  scale  reading  the  reading  of  the 
horizontal  circle  must  be  corrected  by  the  angular  value  of  the 
portion  of  the  scale  included  between  the  observed  scale  reading  and 
the  scale  reading  of  the  axis.  With  magnet  erect  the  zero  of  the 
graduation  is  at  the  apparent  left  and  increasing  scale  readings 
correspond  to  decreasing  circle  readings.  Under  ordinary  conditions 
the  scale  reading  of  the  axis  of  a  magnet  will  remain  very  nearly 
constant  for  a  long  time.  If  it  shows  much  variation  from  station 
to  station,  the  magnet  should  be  examined  carefully  to  make  sure 
that  the  scale  glass  and  its  mounting  are  not  loose. 

The  angular  value  of  one  division  of  the  scale  is  readily  determined 
by  pointing  successively  on  every  fifth  or  every  tenth  division  and 
reading  the  horizontal  circle  in  eac*h  case,  then  repeating  the  opera- 
tions in  the  reverse  order,  so  as  to  eliminate  gradual  change  of 
declination  during  the  observations,  as  shown  in  the  following 
example,  the  order  of  observations  being  indicated  by  the  figures  in 
the  second  and  fourth  column: 

SCALE  VALUE  OF  MAGNET  11L  OP  MAGNETOMETER  No.  11. 


Scale 
reading. 

First  set. 

1 

Second  set. 

Mean. 

Value  of  30 
divisions. 

0 

1 

146  46  45 

12 

146  46  15 

146  46  30 

(0-30) 

10 

2 

146  11  15 

11 

146  10  30 

146  10  52 

(10-40) 

20 

3 

145  33  30 

10 

145  32  30 

145  33  00 

(20-50) 

30 

4 

144  57  45 

9 

144  57  15 

144  57  30 

1  49  00 

40 

5 

144  20  45 

8 

144  20  00 

144  20  22 

1  50  30 

50 

6 

143  42  30 

7 

143  42  30 

143  42  30 

1  50  30 

30  divisions 

1  5000 

1  division 

3'.67 

58 


DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 


The  accompanying  example  showing  the  form  of  record  and  com- 
putation needs  little  explanation. 


Form  37. 


MAGNETIC  DECLINATION. 


Station,  Smyrna  Mills,  Me. 
Magnetometer  No.  20. 
Mark,  Flagpole  on  school  building. 
Magnet,  20L. 


Date,  Friday,  August  5, 1910. 
Observer,  H.  E.  McComb. 

Line  of  detorsion,  80°. 


Chron. 
time. 

Scale. 

Scale  readings. 

Horizontal  circle  readings. 

Left. 

Right.       Mean. 

Mark. 

Magnet. 

A.m. 
923 

9  24 
926 
9  27 
9  28 
9  29 
9  31 
9  32 

E 
E 
I 
I 
I 
I 
E 
E 

d. 

28.8 
28.9 
28.7 
28.7 
28.7 
28.8 
28.5 
28.5 

d.              d. 
30.2          29.50 
30.3          29.60 
25.  6          27.  15 
25.7          27.20 
25.8          27.25 
25.8          27.30 
30.  9          29.  70 
30.  9          29.  70 

i 

Before         A 
B 
After       j    A 
B 

0           1          II 

32538  40 
145  3900 
325  38  40 
145  39  00 

0             /         It 

226  46  20 
46  46  40 
226  4620 
46  46  40 

Mean 

325  38  50 

226  4630 

Mean  scale  readings.         d. 
Erect                                             29.62 
Inverted                                        27.22 

Axis                                               28.42 

Mean  scale  reading,  erect 
Axis 

Scale—  Axis 

Reduction  to  axis 
Circle  reading 

d. 
29.62 
28.42 

Remarks: 
Temp.:  27°.OC. 
Weather:  Fair. 
Torsion    weight    suspended    25 
minutes. 
1  division  of  scale=2'.0. 

h.      m. 
Mean  chron.  time                      9    27.  5 
Chron.  corr'n  on  L.  M.  T.           +27.  3 

+1.20 

226    46.5 

Mag'c  S.  M.  reading 
Mark  reading 

226    48.9 
325    38.8 

Magnetic  azimuth  of  mark 
True  azimuth  of  mark  * 

98    49.9 
78    50.1 

Magnetic  declination,  W 
Diurnal  variation 

19    59.8 
+5.5 

Mean  declination,  W 

20    05.3 

Local  mean  time 

9    55 

*  Counted  from  south  around  by  west  from  0°  to  360°. 

The  azimuth  of  the  mark  and  the  chronometer  correction  on  local 
mean  time  were  obtained  from  the  computation  of  the  observations 
of  the  sun,  reproduced  on  page  51.  The  magnetic  south  meridian 
reading  subtracted  from  the  mark  reading  gives  the  magnetic  azimuth 
of  the  mark,  and  that  subtracted  from  the  true  azimuth  of  the  mark 
gives  the  magnetic  declination,  east  when  plus  and  west  when  minus. 
The  correction  for  diurnal  variation  is  supplied  in  the  Office  from  the 
records  of  the  nearest  magnetic  observatory,  but  its  approximate 
value  may  be  obtained  (except  for  periods  of  magnetic  storms)  from 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION. 


59 


Table  IX,  which  gives  the  average  diurnal  variation  for  different  sea- 
sons of  the  year  for  the  different  observatories. 

India  Magnetic  Survey  pattern  magnetometer. — Magnetometers  of 
the  type  shown  in  Figure  4  are  in  use  at  three  of  the  magnetic  observa- 
tories of  the  Coast  and  Geodetic  Survey.  They  are  very  well  adapted 


FIG.  4.— India  Magnetic  Survey  pattern  magnetometer. 

for  that  purpose,  but  are  rather  too  heavy  for  field  work,  although  one 
of  them  has  been  so  used  for  several  years.  This  type  of  instrument 
was  designed  by  Capt.  H.  A.  Denholm  Fraser,  R.  E.,  for  use  in  the 
magnetic  survey  of  India,  and  is  a  modification  of  the  well-known 
Kew  pattern.  The  long  ma^giietJs^hollow  cylinder  about  9  cm.  long 


or  THE 
UNIVERSITY 


60  DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 

and  1  cm.  in  diameter,  with  an  aluminum  cell  mounted  externally  at 
each  end.  The  cell  at  the  south  end  carries  a  piece  of  optical  glass  on 
which  are  engraved  two  lines  at  right  angles  to  each  other.  The  cell 
at  the  north  end  contains  a  collimating  lens.  On  the  glass  diaphragm 
of  the  reading  telescope  there  are  two  scales,  one  vertical  and  the  other 
horizontal.  Around  the  middle  of  the  magnet  is  a  shallow  groove, 
which  is  engaged  by  a  screw  pin  on  the  under  side  of  the  stirrup.  The 
stirrup  has  another  sheath  above  the  one  holding  the  magnet,  in  which 
is  placed  an  inertia  bar  of  the  same  dimensions  as  the  magnet  when 
observations  are  made  to  determine  the  moment  of  inertia  of  the 
magnet  and  suspension.  The  magnet  is  not  removed  from  the  stirrup 
except  when  repairs  are  necessary.  Four  longitudinal  lines  on  the 
magnet  and  a  mark  on  the  stirrup  insure  the  horizontality  of  one  of 
the  cross  lines  on  the  glass  in  the  s,outh  cell. 

The  short  magnet  is  similar  tow  the  long  magnet,  reduced  in  all 
dimensions,  but  without  the  end  cells.  It  is  mounted  in  a  stirrup 
above  and  parallel  to  an  aluminum  collimator  similar  to  the  long 
magnet.  The  magnets  are  suspended  by  phosphor-bronze  ribbons 
having  about  the  same  coefficient  of  torsion  as  a  silk-fiber  suspension. 
The  torsion  weight  is  a  xylonite  disk  mounted  on  a  metal  spindle.  It 
is  divided  on  the  periphery  to  degrees  and  is  figured  at  every  fifth 
division.  By  the  insertion  of  a  small  lens  in  front  of  the  objective  of 
the  reading  telescope,  the  suspended  weight  may  be  read  without 
change  of  focus.  The  plane  of  detorsion  is  indicated  by  the  zero  of 
the  graduation. 

The  straight  brass  deflection  bar  is  not  graduated,  but  has  a  series 
of  holes  bored  in  its  upper  surface  at  distances  22.5,  26.25,  30,  35,  and 
40  cm.  on  either  side  of  the  center.  During  deflection  observations 
the  long  magnet  is  placed  in  a  small  wooden  box,  on  the  under  side 
of  which  is  a  metal  plug  fitting  snugly  the  holes  in  the  deflection  bar. 
The  box  is  so  constructed  that  the  center  of  the  magnet  is  exactly  over 
the  center  of  this  plug  and  on  a  level  with  the  suspended  short  magnet. 
This  arrangement  eliminates  all  direct  handling  of  the  long  magnet 
during  deflection  observations. 

Declination  observations  with  this  type  of  magnetometer  differ  only 
in  detail  from  those  given  in  the  example.  The  scale  is  on  the  glass 
diaphragm  of  the  reading  telescope  and  the  reduction  to  axis  is 
obtained  by  subtracting  the  mean  of  the  scale  readings  (magnet  erect 
and  magnet  inverted)  from  50,  the  middle  division.  The  difference 
between  the  erect  and  inverted  readings  is  twice  the  angle  between  the 
geometric  and  magnetic  axes  of  the  magnet  and  should  remain  very 
nearly  constant. 

The  angular  value  of  one  division  of  the  scale  may  be  obtained  by 
pointings  on  a  distant  object  instead  of  on  the  magnet. 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION.  61 

Magnetometers  of  other  design  are  so  seldom  used  in  the  field  work 
of  the  Survey  that  it  is  unnecessary  to  describe  them  in  detail.  Men- 
tion may  be  made  of  No.  21,  a  very  small  instrument  weighing  only 
4  kg.,  similar  to  the  one  used  in  the  magnetic  survey  of  France  and 
described  by  Mascart  on  page  212  of  his  "Traite*  de  Magne'tisme  Ter- 
restre,"  and  No.  25,  a  combination  instrument  of  the  Prussian  field 
magnetometer  type,  consisting  of  theodolite,  magnetometer,  decli- 
nometer, and  dip  circle,  all  arranged  for  mounting  von  the  same  base. 
A  description  of  this  instrument  will  be  found  in  "  Results  of  Obser- 
vations made  at  the  Coast  and  Geodetic  Survey  Magnetic  Observatory 
at  Sitka,  Alaska,  1902-1904." 

DECLINATION   FROM   HORIZONTAL   INTENSITY   OBSERVATIONS. 

In  the  directions  for  determining  horizontal  intensity,  given  later 
on,  it  will  be  seen  that  provision  is  made  for  reading  the  scale  of  the 
magnet  and  the  horizontal  circle  in  connection  with  the  observations 
of  oscillations.  This  furnishes  a  check  on  the  regular  declination 
observations  which  immediately  precede  or  foUow,  since  the  change 
in  scale  reading  should  correspond  with  the  change  in  circle  reading; 
or  a  value  of  the  declination  may  be  computed  by  assuming  that  the 
mark  reading  and  the  scale  reading  of  the  axis  are  the  same  as  during 
the  regular  declination  set.  In  the  example  given  it  was  not  necessary 
to  shift  the  setting  of  the  horizontal  circle  between  declination  and 
oscillation  observations,  since  the  axis  reading  was  very  near  the 
middle  division  (30). 

A  value  of  declination  may  also  be  obtained  from  the  two  sets  of 
deflections,  provided  the  short  magnet  is  erect  in  one  set  and  inverted 
in  the  other,  and  provided  also  that  the  position  of  the  instrument  is 
not  disturbed  between  a  set  of  deflections  and  one  of  the  declination 
sets,  so  that  the  mark  reading  may  be  assumed  to  be  unchanged.  The 
observations  are  so  arranged  that  the  horizontal  circle  is  read  when 
the  magnet  is  deflected  by  approximately  equal  amounts  in  opposite 
directions  from  the  magnetic  meridian,  and  the  mean  of  the  readings 
therefore  represents  the  reading  of  the  magnetic  south  meridian, 
which  combined  with  the  mark  reading  gives  the  magnetic  azimuth  of 
the  mark.  In  the  sample  set  of  deflections  on  page  78: 


Mean  of  1,  4,  5,  8 226  29  36 

2,  3,  6,  7 226  29  15 


Magnetic  south  meridian  reading 226  29  26 

Mark  reading,  from  declination  above 325  38  50 


Magnetic  azimuth  of  mark 99  09  24 


62  DIRECTIONS   FOR   MAGNETIC   MEASUREMENTS. 

From  the  second  set  which  followed  with  magnet  inverted : 

O  /         /' 

Mean  of  1,  4,  5,  8 295  32  26 

2,  3,  6,  7 .  295  32  25 


Magnetic  south  meridian  reading 295  32  26 

Mark  reading,  from  second  declination  set 34  08  20 


Magnetic  azimuth  of  mark 98  35  54 

Mean  of  two  sets 98  52  39 

True  azimuth  of  mark ' 78  50  05 

Magnetic  declination,  W 20  02  34 

Diurnal  variation -f-     2  00 

Mean  decimation,  W 20  04  34 

In  this  case  the  horizontal  circle  was  shifted  by  means  of  the  lower 
clamp  between  the  two  sets  of  deflections.  The  difference  between 
the  two  values  of  the  magnetic  azimuth  of  the  mark  represents 
approximately  twice  the  angular  distance  between  the  magnetic  axis 
of  the  short  magnet  and  the  middle  division  of  its  scale. 

B.    WITH   A    COMPASS   DECLINOMETER. 

Two  types  of  compass  declinometer  are  in  use  in  the  Coast  and 
Geodetic  Survey.  The  older  form  is  essentially  an  improved  pris- 
matic compass  with  slit  and  thread  arrangement  for  pointing  on  the 
object  selected  as  a  mark.  It  consists  of  a  cylindrical  brass  bowl 
resting  on  three  foot  screws,  in  the  center  of  which  is  the  pivot  on 
which  the  needle  rests.  The  needle  is  a  flat  (in  the  vertical  plane) 
rectangular  bar  9  cm.  long,  terminating  in  steel  points.  It  is  ex- 
panded at  the  center  to  inclose  an  agate  cup  which  may  be  inserted 
from  either  side,  thus  making  it  possible  to  invert  the  needle.  The 
change  in  balance  of  the  needle  with  change  in  vertical  intensity  is 
corrected  by  means  of  a  small  weight  which  may  be  slid  along  the 
needle.  The  portion  of  the  instrument  which  carries  the  alidade 
forms  the  cover  of  the  bowl  and  may  be  taken  off  and  reversed.  The 
horizontal  circle  has  a  limb  12  cm.  in  diameter  divided  to  10'  and 
read  by  estimation  to  whole  minutes.  The  instrument  is  provided 
with  a  circular  level. 

The  compass  declinometer  is  intended  especially  for  use  by  tri- 
angulation  parties,  where  the  azimuth  is  known  and  time  is  not 
available  for  more  extended  magnetic  observations.  As  the  slit  and 
thread  arrangement  can  not  be  used  for  sighting  on  a  very  distant 
object,  it  is  usual  either  to  place  a  temporary  reference  mark  on  line 
from  the  triangulation  station  to  a  distant  object  by  means  of  a 
theodolite  or  else  to  set  up  the  compass  declinometer  accurately  in 
line  and  use  the  triangulation  station  itself  as  the  reference  mark. 

In  a  perfect  instrument  the  point  of  support  of  the  needle  should 
be  in  the  vertical  of  the  center  of  graduation,  and  the  three  objects — 
the  slit  at  the  prism,  the  point  of  support,  and  the  sight  wire — should 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION. 


63 


be  in  the  same  vertical  plane.  When  this  is  not  the  case,  the  instru- 
ment will  have  an  index  correction,  constant  so  long  as  the  adjust- 
ment of  the  instrument  remains  unchanged,  which  must  be  deter- 
mined at  the  beginning  and  end  of  a  season's  work  at  some  place 
where  the  declination  is  known.  Changing  the  position  of  the  prism, 
i.  e.,  moving  it  up  or  down  on  its  support,  if  the  latter  be  not  truly 
vertical,  will  change  the  index  correction.  When  making  the  ob- 
servations to  determine  the  index  correction,  therefore,  the  observer 
should  mark  the  position  of  the  prism  and  in  subsequent  observa- 
tions should  be  sure  that  it  is  in  the  same  position. 


Form  38. 

MAGNETIC  DECLINATION. 

Station,  Cheltenham,  Md. 
Compass  Declinometer  No.  741. 
Mark,  Hill's  barn  cupola. 


Date,  Monday,  February  28,  19 10. 
Observer,  J.  E.  Burbank. 


Chron. 
time, 
a.  m. 

Mark. 

Circle  direct. 
Needle  direct. 

Circle  reversed. 
Needle  inverted. 

Mark. 

North  end. 

South  end. 

South  end. 

North  end. 

A.    TO. 

0           / 

0          / 

0             , 

0          f 

0          / 

0            , 

11  24 

257  08 

183  05 

2  54 

182  54 

2  57 

257  09 

77  06 

3  04 

182  54 

2  53 

182  57 

7706 

257  10 

182  54 

2  57 

183  02 

2  59 

257  06 

11  40 

7708 

2  53 

18256 

3  00 

18257 

77  04 

Means 

257  08.  0 

182  59.0 

182  55.  2 

182  57.  2 

182  57.  5 

257  06.2 

p.  m. 

h.  TO. 

16  13 

17  06 

302  50 

122  49 

122  40 

302  38 

17  03 

197  04 

122  50 

302  48 

30238 

12237 

197  02 

17  04 

302  48 

122  49 

122  48 

302  35 

17  04 

16  28 

197  02 

122  49 

302  48 

302  44 

122  34 

197  02 

Means 

17    04.0 

302  49.  2 

302  48.5 

302  42.5 

302  36.0 

17  02.8 

Chron.  correction  on  star 
Difference  of  longitude,  ; 

Chron.  correction  on  loca 

idard  75th  m 
°50'  

h.  m. 
er.  time*  ..                         —2  25 

7 

1  mean  time 

n 

—2  32 

Local  mean  time. 

h.       m. 
9        00 

ft.         TO. 

13      48 

Remarks. 

1 

Mark  reading 

257  07.  1 

1703.4 

-.-,      ,-.-•;. 

Needle  reading 

182  57.  2 

302  44.  1 

Magnetic  azimuth  of  mark 

74  09.9 

74  19.3 

True  azimuth  of  mark  f 

68  51.3 

68  51.3 

..                 . 

Magnetic  declination,  W 

5  18.6 

5  28.0 

Index  correction 

+14.4 

+14.4    i 

Diurnal  var.  correction 

+  2.0 

-  5.0 

Resulting  declination,  W 

5  35.0 

5  37.4 

*  Plus  when  slow,  minus  when  fast. 


t  Counted  from  south  around  by  west. 


64  DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 

After  leveling  the  instrument  and  adjusting  the  position  of  the 
prism,  the  vertically  of  the  sight  wire  should  be  tested  by  means  of 
a  plumb  line  or  the  vertical  edge  of  a  building.  The  mark  selected 
should  be  nearly  in  the  horizon,  so  that  the  error  due  to  lack  of  ver- 
ticality  of  the  wire  may  be  as  small  as  possible. 

Place  the  needle  on  the  lifter,  close  the  box,  and  lower  the  needle 
gently  onto  the  pivot.  Adjust  the  balance  if  necessary  by  means  of 
the  sliding  weight.  The  order  of  observations  will  then  be  as  follows, 
both  indices  being  read  in  each  case:  (1)  Two  pointings  on  the  mark; 
(2)  one  pointing  on  the  north  end  of  the  needle;  (3)  one  pointing  on 
the  south  end  of  the  needle;  (4)  one  pointing  on  the  south  end  of  the 
needle;  (5)  one  pointing  on  the  north  end  of  the  needle;  (6)  invert 
the  needle  and  reverse  the  upper  part  of  the  instrument;  (7)  one 
pointing  on  the  south  end  of  the  needle;  (8)  one  pointing  on  the 
north  end  of  the  needle;  (9)  one  pointing  on  the  north  end  of  the 
needle;  (10)  one  pointing  on  the  south  end  of  the  needle;  (11)  two 
pointings  on  the  mark.  The  needle  should  be  disturbed  slightly 
between  readings  (3)  and  (4)  and  (8)  and  (9)  by  means  of  a  piece  of 
steel  (screw  driver  or  knife). 

Record  the  times  of  beginning  and  ending  of  the  pointings  on  the 
needle  and  give  the  correction  of  the  timepiece  on  standard  tune. 
It  is  preferable  to  make  observations  both  morning  and  afternoon  at 
about  the  tunes  when  the  easterly  and  westerly  extremes  of  declina- 
tion ordinarily  occur  or  late  in  the  afternoon  when  the  reduction  to 
mean  of  day  is  usually  small.  (See  Table  IX.)  If  time  permits, 
three  sets  of  observations  should  be  made,  shifting  the  position  of 
the  foot  screws  on  the  tripod  between  sets. 

While  in  theory  the  above  type  of  compass  declinometer  has  many 
points  to  commend  it,  in  practice  it  has  not  proved  entirely  satis- 
factory. In  two  cases  the  index  correction  has  been  found  to  be 
different  for  different  positions  of  the  needle  with  respect  to  the  bowl, 
indicating  the  presence  of  magnetic  impurities  in  the  metal  of  which 
the  bowls  are  constructed,  although  special  tests  have  failed  to  detect 
the  seat  of  the  trouble. 

In  supplying  the  demand  for  additional  compass  declinometers,  the 
satisfactory  results  which  have  been  obtained  in  determining  the 
declination  with  compass  attachments  fitted  to  dip  circles  have  led 
to  the  construction  of  a  new  type  of  instrument  from  designs  prepared 
by  Mr.  E.  G.  Fischer,  Chief  of  the  Instrument  Division.  It  is  nothing 
more  than  a  compass  needle  with  peep  sights  mounted  on  a  graduated 
horizontal  circle,  but  some  of  the  details  are  novel  and  all  have  been 
worked  out  with  great  care.  The  base  rests  on  three  leveling  screws, 
has  double  centers,  and  the  horizontal  circle  is  read  by  two  verniers. 
This  base  supports  a  rectangular  box,  in  which  is  mounted  a  compass 


DETERMINATION  OF  THE  MAGNETIC  DECLINATION. 


65 


needle  about  6  inches  long.  At  each  end  of  the  needle  is  a  graduated 
arc,  about  20°  in  extent,  with  the  zero  in  the  middle.  Vertical  peep 
sights  are  attached  to  the  ends  of  the  box,  so  that  the  zeros  of  the 
graduations  and  the  point  of  support  of  the  needle  are  in  the  vertical 
plane  through  the  peep  sights.  The  lifter  of  the  needle  is  of  special 
design,  so  arranged  that  the  instrument  can  not  be  packed  for  ship- 
ment without  first  lifting  the  needle  off  the  pivot.  Observations  with 
this  type  of  instrument  differ  but  little  from  those  described  in  detail 
for  the  older  form  of  declinometer. 

The  instrument  should  be  set  low  enough  to  permit  the  observer  to 
look  directly  down  upon  the  needle  when  making  the  settings.  After 
the  instrument  has  been  leveled  and  the  sliding  weight  adjusted  in 
position  if  necessary,  the  order  of  observations  is  as  follows:  (1)  Two 
pointings  on  the  mark,  one  direct  and  one  reversed;  (2)  one  reading, 
north  end  of  needle  set  at  zero;  one  reading,  south  end  set  at  zero; 
one  reading,  south  end  set  at  zero;  one  reading,  north  end  set  at  zero. 
In  a  similar  manner  (3)  four  readings  with  north  end  set  5°  east  of 
zero  or  south  end  5°  west  of  zero;  (4)  four  readings  with  north  end  5° 
west  of  zero  or  south  end  5°  east  of  zero;  (5)  four  readings  with  the 
ends  set  at  zero;  (6)  two  pointings  on  the  mark.  Record  must  be 
made  of  the  time  of  beginning  and  ending.  It  will  be  sufficient  to 
read  one  vernier  for  settings  on  one  end  of  the  needle  and  the  other 
vernier  for  settings  on  the  other  end.  The  needle  should  be  lifted 
when  pointing  on  the  mark.  The  eye  should  be  moved  up  and  down 
the  slit  to  insure  accuracy  of  pointing. 

Observations  with  the  compass  attachment  of  a  dip  circle  (shown 
in  Fig.  5)  are  made  in  the  same  manner  and  the  method  of  computa- 
tion is  in  each  case  the  same  as  for  the  older  form  of  declinometer.  A 
sample  set  of  observations  is  given  below. 


Form  38a. 


MAGNETIC  DECLINATION. 


Station,  Sweetwater,  Tex. 
Compass  of  dip  circle  No.  30. 
Mark,  Cupola  of  schoolhouse. 


Date,  January  17, 1910. 
Observer,  W.  H.  Burger. 


Chron.  time. 

Mark, 
circle 
direct. 

Needle  set  at  0°. 
set  at  0°. 

Needle  set  5°  right, 
set  5°  left. 

Mark, 
circle 
reversed. 

North  end. 

South  end. 

North  end. 

South  end. 

h.  m. 
1032 

13  05 

21  24 

21  25 

16  27 

16  25 

13  01 

23 

23 

26 

24 

23 

26 

26  19 

26  18 

10  40 

13  05 

24 

25 

20 

18 

13  04 

Means. 

13  05.  0 

21  23.5 

21  24.8 

21  23.0 

21  21.2 

13  02.  5 

77213—11- 


66  DIRECTIONS   FOE  MAGNETIC    MEASUREMENTS. 

DETERMINATION  OF  THE  DIP. 
A.    WITH  A  DIP  CIRCLE. 

The  dip  or  inclination  is  usually  measured  by  means  of  a  dip  circle, 
in  which  a  magnetized  needle  is  mounted  in  such  a  way  as  to  swing 
in  a  vertical  plane  about  an  axle  through  its  center  of  gravity.  The 
form  of  dip  circle  in  general  use  is  the  Kew  pattern  shown  in  Figure  5. 
The  pivots  of  the  needle  rest  on  agate  knife  edges,  the  supports  of 
which  are  horizontal  or  vertical  according  as  the  instrument  is  intended 
for  use  in  high  or  low  magnetic  latitudes.  The  needle  is  placed  in 
position  by  means  of  a  lifter  so  arranged  that  when  the  needle  is 
lowered  onto  the  agate  knife  edges,  the  prolongation  of  the  axis  of 
the  pivots  passes  through  the  center  of  the  graduated  vertical  circle. 
The  vertical  circle  is  read  by  two  verniers,  and  in  older  instruments 
is  usually  graduated  from  zero  at  either  side  to  90°  at  the  top  and 
bottom.  Some  of  the  more  modern  dip  circles  are  graduated  con- 
tinuously from  zero  to  360°.  To  the  frame  carrying  the  verniers  are 
attached  two  microscopes  for  pointing  on  the  ends  of  the  needle,  so 
placed  that  when  the  circle  reading  is  zero  the  line  joining  the  micro- 
scopes is  horizontal.  On  the  frame  carrying  the  microscopes  are 
blocks  for  holding  in  position  the  needle  used  as  a  deflector  in  the 
determination  of  total  intensity  by  Lloyd's  method,  so  arranged  that 
when  the  needle  is  in  position  its  axis  is  at  right  angles  to  the  line 
joining  the  microscopes.  Four  needles  are  usually  provided,  two 
for  regular  dip  observations  and  two  for  the  determination  of  total 
intensity. 

Some  of  the  newer  dip  circles  of  this  pattern  are  provided  with  a 
compass  needle  mounted  in  a  rectangular  box,  which  may  be  placed 
on  top  of  the  dip  circle  as  shown  in  Figure  5.  The  angle  between  the 
magnetic  meridian  as  defined  by  the  compass  needle  and  the  line  to 
some  mark  of  which  the  true  bearing  is  known  may  be  measured  with 
the  aid  of  peep  sights. 

In  dip  circles  of  the  Lloyd-Creak  pattern  (Fig.  9),  designed  for 
observations  on  shipboard,  but  suitable  also  for  land  observations, 
the  pivots  of  the  needle  rest  in  agate  cups  instead  of  on  agate  knife 
edges  and  the  ends  of  the  needle  are  in  close  proximity  to  the  gradu- 
ated circle  so  that  the  end  of  the  needle  and  the  adjacent  graduation 
are  seen  through  the  reading  microscope  at  the  same  time. 

In  dip  circles  of  the  Brunner  pattern  a  movable  graduated  circle  is 
immediately  behind  the  needle  and  carries  at  the  opposite  extremities 
of  a  diameter  two  small  concave  mirrors,  the  centers  of  which  are  as 
far  apart  as  the  points  of  the  needle.  A  setting  is  made  by  revolving 
the  graduated  circle  until  the  point  of  the  needle  and  its  reflected 
image  coincide.  The  angle  of  dip  is  then  read  off  on  a  fixed  vernier. 

The  adjustment  of  a  dip  circle  is  usually  made  with  care  in  the 
instrument  shop  before  the  instrument  is  sent  into  the  field  and 


DETERMINATION   OF   THE  DIP. 


67 


seldom  requires  attention  in  the  course  of  a  season's  work.  As  cases 
may  arise,  however,  where  it  is  important  to  make  adjustments  in 
the  field,  the  following  directions  are  given. 


FIG.  5. — Kew  pattern  dip  circle. 


The  bearing  surfaces  of  the  agate  knife  edges  should  lie  in  a  hori- 
zontal plane  which  if  produced  would  pass  below  the  center  of  gradu- 
ation of  the  vertical  circle  at  a  distance  equal  to  the  radius  of  the 
pivots  of  the  needles.  A  small  level  is  provided  to  assist  in  making 


68  DIRECTIONS  FOR  MAGNETIC    MEASUREMENTS. 

this  adjustment.  The  height  of  the  agate  surfaces  with  reference  to 
the  center  of  graduation  may  be  tested  by  placing  the  needle  in  posi- 
tion and  keeping  it  nearly  horizontal  by  a  strip  of  wood  or  piece  of 
stiff  paper  under  the  north  end.  If  the  two  ends  read  the  same  (or 
180°  apart,  if  the  vertical  circle  is  graduated  to  360°)  the  needle  is  at 
the  proper  height.  Readings  should  be  made  in  both  positions  of  the 
microscopes  to  be  sure  that  they  are  placed  exactly  180°  apart  and 
in  both  positions  of  the  needle,  face  east  and  face  west,  to  correct  for 
lack  of  symmetry. 

The  lifter  should  be  adjusted  so  that  when  the  needle  is  lowered  on 
to  the  agate  surfaces  its  pivots  will  both  touch  at  the  same  time  and 
its  axis  of  rotation  if  produced  would  pass  through  the  center  of 
graduation  of  the  vertical  circle,  so  that  the  needle  will  rotate  in  a 
plane  parallel  to  the  graduation.  The  vertical  line  through  the  center 
of  graduation  may  be  determined  by  suspending  a  small  plumb  bob 
at  the  end  of  a  silk  fiber,  so  that  the  fiber  intersects  the  graduation  at 

two  points  exactly 
's  180°  apart.  A  small 
movable  hook  is  pro- 
vided for  this  pur- 
pose in  the  top  of 
most  dip  circles. 

The     microscopes 
for  pointing  on  the 

FIG.  6.-Remagnetization  of  dip  needle.  en(jg    Qf    ^     neecQe 

should  be  exactly  180°  apart  and  should  be  focused  for  clear  vision 
before  beginning  observations. 

To  avoid  the  necessity  of  carrying  a  separate  tripod  for  the  dip 
circle,  an  extra  head  is  usually  provided,  which  can  be  fastened  on  top 
of  the  magnetometer  tripod  when  dip  observations  are  to  be  made. 
When  the  dip  circle  has  been  placed  in  position  its  level  is  adjusted 
and  the  instrument  leveled  in  the  usual  way. 

The  observer  should  have  constantly  in  mind  the  necessity  of 
guarding  the  needles  from  falls  or  other  accidents  and  keeping  them, 
especially  the  pivots,  clean  and  free  from  rust.  The  pivots  are  best 
cleaned  by  sticking  them  into  a  piece  of  pith.  Before  beginning 
observations,  the  bearing  surfaces  of  the  agates  should  also  be  cleaned 
with  the  edge  of  a  piece  of  paper  or  with  pith. 

The  polarity  of  the  dip  needles  must  be  reversed  before  beginning 
a  set  of  observations  as  well  as  in  the  middle  of  the  set.  This  opera- 
tion is  performed  in  the  following  manner:  Place  one  needle  on  the 
reversing  block  after  having  determined  which  end  is  attracted  down- 
ward (north  end).  Take  one  bar  magnet  north  end  down  in  one 
hand,  and  the  other  magnet  south  end  down  in  the  other  hand,  each 
inclined  about  30°  to  the  horizon.  Draw  the  magnets  lightly  from 


DETERMINATION   OF   THE  DIP.  69 

center  to  end  of  the  needle,  the  magnet  with  north  end  down  resting 
on  the  end  of  the  needle  which  was  attracted  downward.  Make  5 
strokes,  then  interchange  the  magnets  and  make  5  more.  Then  turn 
the  needle  over  and  repeat  the  operation,  making  20  strokes  in  all. 
Care  must  be  taken  to  stroke  the  same  end  of  the  needle  with  the 
north  end  of  the  magnets  throughout  the  operation. 

The  next  step  is  to  determine  the  plane  of  the  magnetic  meridian 
and  the  corresponding  reading  of  the  horizontal  circle.  If  the 
instrument  is  provided  with  a  compass  attachment,  the  magnetic 
meridian  is  readily  determined  by  mounting  the  compass  and  turning 
the  instrument  until  the  compass  needle  points  to  zero.  The  instru- 
ment, that  is,  the  plane  of  the  vertical  circle,  is  then  in  the  magnetic 
meridian,  and  the  reading  of  the  horizontal  circle,  as  well  as  the  one 
differing  by  180°,  is  the  one  at  which  the  circle  is  to  be  set  when 
making  dip  observations.  Care  must  be  taken  to  remove  the  com- 
pass attachment  before  the  dip  observations  are  made,  otherwise  the 
results  will  be  vitiated. 

In  case  no  compass  attachment  is  available,  or  in  high  magnetic 
latitudes,  where  the  compass  needle  is  sluggish,  the  magnetic  meridian 
may  be  determined  by  taking  advantage  of  the  fact  that  when  a  dip 
needle  is  mounted  in  a  plane  at  right  angles  to  the  magnetic  meridian 
it  will  stand  vertical.  Raise  the  lifter,  place  one  of  the  needles  upon 
it  with  its  "face"  toward  the  reading  microscopes.  (The  face  of  the 
needle  is  the  side  on  which  the  letters  A  and  B  are  engraved.)  Set 
the  upper  vernier  at  90°  and  place  the  instrument  at  right  angles  to 
the  meridian,  with  the  vertical  circle  toward  the  north.  Lower  the 
needle  onto  the  agates  and  bring  it  nearly  to  rest  by  means  of  succes- 
sive liftings  and  lowerings.  Turn  the  instrument  in  azimuth  until 
the  swing  of  the  upper  end  of  the  needle  is  bisected  by  the  cross  hair 
of  the  upper  microscope,  gently  lifting  and  lowering  the  needle  several 
times  to  make  sure  that  it  is  swinging  freely.  Record  the  reading 
of  the  horizontal  circle.  Set  the  lower  vernier  at  zero  and  repeat  the 
operation,  pointing  on  the  lower  end  of  the  needle.  Then  turn  the 
instrument  180°  in  azimuth  and  repeat  the  operations,  beginning  with 
the  lower  end  of  the  needle.  The  mean  of  the  four  readings  of  the 
horizontal  circle  is  the  reading  of  the  magnetic  prime  vertical,  and  as 
the  circle  is  usually  graduated  by  quadrants  from  0°  to  90°,  the  read- 
ings of  the  magnetic  meridian  will  be  the  same.  The  dip  observations 
proper  may  then  be  begun.  It  is  usual  to  observe  with  two  needles 
at  each  station,  and  the  work  is  so  arranged  that  the  middle  time  of 
observation  is  the  same  for  each  needle.  Observations  should  be 
begun  with  the  needle  which  was  magnetized  first. 

Place  the  instrument  in  the  magnetic  meridian,  (vertical)  circle 
east,  needle  face  east,  and  reduce  the  swing  of  the  needle  to  a  small 
arc  by  means  of  successive  liftings,  noting  at  the  same  time  whether 


70  DIRECTIONS   FOB   MAGNETIC    MEASUREMENTS. 

the  swing  of  the  needle  appears  to  be  free  and  regular.  (If  such  is  not 
the  case,  the  pivots  and  agates  should  be  cleaned  again.)  Set  on  the 
upper  (south)  end  of  the  needle  and  read  the  upper  vernier;  then  set 
on  the  lower  (north)  end  and  read  the  lower  vernier;  then  record  the 
two  readings.  Better  results  are  obtained  if  the  needle  is  observed 
while  swinging  over  a  small  arc,  but  it  should  not  be  disturbed  between 
the  readings  of  the  two  ends,  so  that  the  swing  at  the  time  of  the  first 
reading  should  be  just  sufficient  to  continue  until  the  second  has  been 
made.  The  needle  is  then  lifted  and  lowered  and  the  two  ends  read 
in  the  reverse  order.  In  general  the  two  ends  of  the  needle  will  not 
read  the  same,  but  the  difference  between  the  two  should  be  nearly 
constant  for  a  particular  position  of  circle  and  needle.  If  such  is  not 
the  case,  or  if  the  readings  before  and  after  lifting  differ  by  as  much  as 
8',  the  readings  should  be  repeated. 

The  circle  is  then  turned  180°  in  azimuth  and  similar  readings  are 
taken  hi  the  position  circle  west,  needle  face  west.  Then  the  needle 
is  turned  over  and  observations  made  with  circle  west,  needle  face 
east,  and  finally  the  circle  is  reversed  again  and  readings  are  taken  in 
the  fourth  position  circle  east,  needle  face  west.  The  same  operations 
are  then  performed  with  needle  No.  2. 

Next  the  polarities  of  the  two  needles  are  reversed,  so  that  the  end 
which  was  down  before  will  now  be  up,  and  a  second  half  set  of  obser- 
vations is  made,  with  No.  2,  followed  by  a  second  half  set  with  No.  1. 
The  tunes  of  beginning  and  ending  should  be  noted  for  each  needle. 

The  mean  of  all  the  readings  gives  the  resulting  dip,  unless  there 
is  much  difference  in  the  results  before  and  after  reversal  of  polarities, 
in  which  case  a  small  correction  is  required  (Table  VIII),  as  explained 
on  page  13.  The  computation  is  arranged  for  simplicity  in  such  a 
way  that  means  of  two  quantities  are  taken  successively,  so  that  the 
work  may  be  performed  mentally. 

In  case  the  vertical  circle  is  graduated  continuously  from  zero  to 
360°,  it  will  be  necessary  to  subtract  the  circle  readings  from  180° 
or  360°  for  circle  west  in  order  to  get  the  angle  of  dip. 


DETERMINATION   OF   THE   DIP. 


71 


Form  42. 


MAGNETIC  DIP. 


Station,  Smyrna  Mills,  Me. 

Dip  circle  No.  5678.    Needle  No.  2. 


Date,  Friday,  August  5, 1910. 
Observer,  H.  E.  McComb. 


End  of  needle  marked  A  down. 

Circle  east. 

.   Circle  west.               Circle  west.                Circle  east. 

Needle  face  east. 

Needle  face  west.      Needle  face  east.       Needle  face  west. 

S. 

N. 

1 
S.               N.               S.               N.               S.               N. 

, 

75  19 
22 

7520 
22 

75  39      !     75  41           75  45           75  39           74  52         75  04 
41                43                48                41                51              03 

7520.5 

75  21.0 

7540.0!     7542.0       7546.5       7540.0       7451.5     7503.5 

1                                             ! 

75  20.8 
75  31 

75  41.  0                          75  43.  2                         74  57.  5 
3.  9                                                                   75  20.  4 
Mean:  75°  25/.6 

Polarities  reversed.    End  of  needle  marked  B  down. 

Circle  east. 

Circle  west.            Circle  west.                  Circle  east. 

Needle  face  east. 

Needle  face  west.       Needle  face  east.       Needle  face  west. 

S.               N. 

S.               N.               S.               N.              S.               N. 

7504 
02 

7512 
10 

75  52          75  46          75  41          75  45          75  15        75  13 

55                49                41                44                14              14 

75  03.0 

75  11.0 

7553.5       7547.5       75  41.0  j    7544.5       7514.5     7513.5 

75  07.0 
752 

75  50.5                          75  42.S                          75  14.0 
;.8                                                                7528.4 
Mean:  75°  28'.  6 

Resulting  dip:  75°  27'.  1 

Chron.  time  of  begii 
"    "    end 

Mean  chronometer 
Chron.  correction  01 

Local  mean  time 
Magnetic  meridian 

h.m.    '        Instrument  in  mag.  prime  vertical, 
ming              2  10 

'ms                2a2      Vertical             Vwidlp              Hor.  circle 
circle.               -Needle.              readings. 

bime                2  21                                                        1 

i  L.  M.  T.     +  27 
North      S.  end  at  90°                   55  48 
2  *            "          N.  end  at  90°                   56  15 
•     .   South      N.  end  at  90°                   55  14 
«          S.  end  at  90°                    55  50 

reads             55  47                                           Mean              55  47 

72 


DIRECTIONS   FOR    MAGNETIC    MEASUREMENTS. 


B.    WITH    AN    EARTH   INDUCTOR. 

A  small  earth  inductor  of  the  type  designed  by  Wild  is  shown  in 
Figure  7.  The  coil  is  rotated  by  means  of  a  gear  and  piece  of  flexible 
shafting.  A  sudden  starting  or  stopping  of  the  rotation  must  be 
avoided,  as  it  is  apt  to  break  the  flexible  shaft.  The  galvanometer 
should  be  mounted  in  a  position  where  it  can  be  observed  conveniently 
while  rotating  the  coil.  The  axis  of  the  vertical  circle  is  leveled  by 
means  of  a  stride  level  and  the  axis  of  the  coil  is  placed  in  the  mag- 
netic meridian  by  means  of  a  compass  attachment.  The  observations 
for  determining  the  dip  are  made  in  the  following  manner : 


Fio.  7.— Wild  pattern  earth  inductor. 

(1)  With  vertical  circle  east,  place  the  axis  of  the  coil  vertical  by 
means  of  the  level  inside  the  coil  and  read  the  vertical  circle,  first 
with  face  of  coil  marked  A  east,  then  with  face  marked  B  east. 

(2)  Place  the  axis  of  coil  approximately  in  the  line  of  dip,  rotate 
the  coil,  and  observe  the  galvanometer.     If  the  instrument  is  set 
accurately  in  the  magnetic  meridian,  the  galvanometer  will  be  deflected 
steadily  in  one  direction.     If  it  is  not  quite  in  the  meridian,  the  gal- 
vanometer will  be  deflected  a  small  amount  in  one  direction,  and  then 
as  the  speed  of  rotation  increases  will  go  off  in  the  opposite  direction. 
By  successive  trials  find  the  setting  at  which  no  deflection  of  the 
galvanometer  is  produced  when  the  coil  is  rotated.     Record  the  time 
and  the  reading  of  the  vertical  circle.     Rotate  the  coil  in  the  opposite 
direction,  make  another  setting,  and  read  the  vertical  circle.     Make 


DETERMINATION   OF   THE   DIP. 


73 


two  more  settings,  one  for  rotation  in  each  direction.  The  circle 
should  be  clamped  when  the  coil  is  being  rotated.  After  the  first 
reading  the  changes  in  setting  can  be  made  with  the  tangent  screw. 
The  operation  will  be  facilitated  if  the  crank  for  rotating  the  coil  is 
supported  so  that  one  hand  may  be  free  to  move  the  tangent  screw 
while  the  other  rotates  the  coil. 

(3)  Place  the  axis  of  the  coil  vertical  again,  and  read  the  vertical 
circle  in  two  positions  of  the  coil. 

(4),  (5),  and  (6)  Proceed  in  the  same  manner  with  vertical  circle 
west. 

The  difference  between  the  circle  readings  for  axis  vertical  and  axis 
inclined  gives  the  co-dip.  The  form  of  observation  and  computation 
is  shown  in  the  following  example: 


Form  407. 


Station,  Sitka,  Alaska. 
Earth  inductor  No.  2. 


MAGNETIC  DIP. 


Date,  February  5, 1908. 
Observer,  H.  M.  W.  Edmonds. 


Magnetic  meridian  reads:  10°  40'. 


Vertical  circle  east. 

Vertical  circle  west. 

AXIS  VERTICAL. 

Coil. 

(Order).         A.             B. 

Mean. 

Coil.    !  (Order).         A. 

B.     l  Mean. 

!           i 

i 

0         /                               1 

-.  t 

0 

/            /            / 

A-E 

Begin            0  11.  0        10.  9 

11.0 

A-E      Begin            0  0 

9.  2         09.  2       09.  2 

B-E           (1)                 10.8         10.8 

10.8 

B-E          (4)                0 

9.  9        09.  9       09.  9 

A-E 

End                  11.0        10.9 

11.0 

A-E      End                  09.9  |      09.8       09.8 

B-E           (3)                 10.9         10.8 

10.8 

B-E           (6)                 0 

9.9'      09.7      ,09.8 

Mean 

0  10.9 

Mean       0  09.  7 

AXIS  INCLINED. 

Rot. 

Chron.           A.             B. 

Mean. 

Rot.    i   Chron.          A. 

B.        Mean. 

h.    m.      °        '-:/           ' 

, 

h.     m.        ° 

/             /            / 

+ 

9     34     344  44.  5         44.  1 

44.3 

+            9      46       15  3 

2.  1        32.  1       32.  1 

- 

(2)                 52.  0        52.  0 

52.0 

(5)                 3 

J.  0        33.  0       33.  0 

+ 

45.  7        45.  3 

45.5 

+                                 3 

3.0        33.0       33.0 

- 

9     40            51.8         51.8 

51.8 

9      49            3 

1.  9        32.  0       32.  0 

Mean     9     37                                 344  48.  4 

Mean    9      48 

15  32.  5 

Dip 

74  37.5 

Dip        7437.2 

Mean  dip  74°  37'.35 

h.  m. 

Mean  chronometer  time  .  .  9  42 

Chronometer  correction  .  .  —  5 

Local  mean  tiir 

e  9  37 

74  DIBECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

DETERMINATION  OF  THE  HORIZONTAL  INTENSITY. 

As  already  explained,  the  determination  of  the  horizontal  inten- 
sity involves  two  operations  called  li oscillations"  and  " deflections." 
The  observations  at  a  station  usually  comprise  two  sets  of  each, 
arranged  in  the  order:  Oscillations,  deflections,  deflections,  oscilla- 
tions. They  are  made  with  a  magnetometer,  two  types  of  which 
have  been  described,  and  as  they  usually  follow  a  set  of  declination 
observations  it  may  be  assumed  that  the  instrument  is  in  adjust- 
ment, that  the  torsion  has  been  removed  from  the  fibers,  and  that 
the  long  magnet  is  suspended. 

TORSION   OBSERVATIONS. 

Point  approximately  on  the  middle  division  of  the  scale  of  the 
magnet,  reduce  the  arc  of  vibration  to  two  divisions  or  less,  and 
read  the  horizontal  circle.  Read  the  torsion  circle  at  the  top  of  the 
suspension  tube  and  the  scale  of  the  magnet  at  the  extremes  of  its 
swing,  as  in  declination  observations,  and  record  the  readings  in  the 
place  provided  on  the  form.  Turn  the  torsion  head  90°  to  the  right 
and  read  the  scale  of  the  magnet.  Turn  the  torsion  head  180°  to 
the  left  (i.  e.,  90°  to  the  left  of  its  original  position)  and  again  read 
the  scale.  Turn  the  torsion  head  90°  to  the  right  and  read  the  scale. 
The  torsion  circle  now  reads  the  same  as  at  the  beginning,  and  the 
last  scale  reading  should  be  very  nearly  the  same  as  the  first.  The 
differences  between  successive  scale  readings  give  the  effect  of  90°, 
180°,  and  90°  of  torsion,  respectively,  in  scale  divisions,  and  their 
sum  divided  by  four  and  multiplied  by  the  arc  value  of  one  division 
of  the  magnet  scale  is  the  average  effect  of  90°  of  torsion,  the  quan- 
tity h  required  to  correct  the  time  of  one  oscillation  for  effect  of 
torsion. 

OSCILLATIONS. 

The  oscillations  are  usually  arranged  in  such  a  way  as  to  give  six 
or  eight  independent  determinations  of  the  time  of  a  selected  number 
of  oscillations,  which,  for  convenience  in  computing,  should  be  some 
multiple  of  10.  Increase  the  arc  of  vibration  to  about  20  divisions, 
10  on  either  side  of  the  middle,  and  determine  the  approximate 
time  of  one  oscillation  by  counting  the  number  of  seconds  required 
for  four  or  six  oscillations,  and  from  that  compute  the  time,  approxi- 
mating half  a  minute,  which  would  be  required  for  some  odd  num- 
ber of  oscillations.  In  the  example  six  oscillations  took  about  34 
seconds.  Hence  the  time  of  five  oscillations  would  be  about  28  sec- 
onds. The  observer  then  arranged  his  program  to  observe  every 
fifth  oscillation  from  0  to  35  and  from  50  to  85,  thus  obtaining  eight 
independent  determinations  of  the  time  of  50  oscillations.  When 


DETERMINATION  OF  THE  HORIZONTAL  INTENSITY.  75 

the  observing  program  has  been  outlined  in  the  first  column  of  the 
form  the  succeeding  operations  are  as  follows:  Read  the  ther- 
mometer and  the  scale  of  the  magnet.  Note  and  record  on  the 
first  line  of  the  second  column  of  the  form  the  time  when  the  middle 
division  of  the  scale  of  the  magnet  crosses  the  vertical  line  of  the 
reading  telescope,  the  magnet  swinging  from  left  to  right.  About 
28  seconds  later  note  and  record  the  time  when  the  middle  division 
of  the  scale  crosses  the  vertical  line,  magnet  swinging  from  right  to 
left,  and  so  on  at  intervals  of  about  28  seconds  until  eight  readings 
have  been  taken.  Then  read  the  thermometer  and  scale  again. 
Compute  approximately  the  time  when  the  fiftieth  oscillation  may  be 
expected,  and  when  that  time  arrives  begin  a  second  series  of  eight 
readings  at  intervals  of  about  28  seconds.  At  the  close  read  the 
thermometer  and  the  scale  of  the  magnet  again.  This  completes  a 
set  of  oscillations.  By  this 
method  it  is  necessary  to 
look  in  the  reading  telescope 
for  only  a  few  seconds  at 
the  time  of  each  observation. 
A  few  seconds  before  the 
predicted  time  of  transit  the 
observer  picks  up  the  beat 
of  the  chronometer  and  be- 
gins to  count  half  seconds 

.  FIG.  8.— Four  and  six  oscillations. 

and  then  looks  into  the  read- 
ing telescope  and  waits  for  the  transit  to  occur.  Thus,  for  the  fifth 
oscillation  he  might  pick  up  the  beat  at  9h  38m  35s  and  count:  Half- 
six — half  -  seven — half  -  eight — half  -  nine — half  -  ten — half-one — half - 
two — half-three,  the  transit  occurring  between  half  and  three.  The 
fraction  of  the  half  seqond  can  best  be  estimated  by  noting  mentally 
the  relative  position  of  the  middle  division  and  the  vertical  line  of 
the  telescope  for  the  beats  just  before  and  after  the  transit  and 
dividing  up  the  half  second  in  the  same  proportion  that  the  space 
is  divided  by  the  position  at  transit.  It  will  usually  be  possible 
to  hear  the  beat  of  the  chronometer  while  observing,  but  in  case 
this  is  prevented  by  noise  the  observer  can  with  a  little  practice 
learn  to  count  the  half  seconds  accurately  without  hearing  the  tick 
for  the  short  interval  involved.  The  chronometer  should  be  kept 
far  enough  from  the  magnet  to  guard  against  the  disturbing  effect 
of  the  steel  spring,  etc. 

DEFLECTIONS. 

Place  the  deflection  bars  in  position,  remove  the  long  magnet  from 
the  stirrup  and  suspend  the  short  magnet  in  its  place  with  scale  erect; 
taking  care  to  keep  the  two  at  least  20  cm.  apart.  Remove  the 


76  DIRECTIONS   FOE  MAGNETIC    MEASUREMENTS. 

thermometer  from  the  magnet  house  and  plug  up  the  hole.  Remove 
the  thermometer  from  its  case  (if  it  is  in  one)  and  place  it  inside  the 
east  deflection  bar.  Place  the  long  magnet  with  scale  erect  and  north 
end  east  at  the  shorter  distance  on  the  east  bar  and  the  torsion  weight 
as  a  counterpoise  on  the  west  bar.  Be  sure  that  the  short  magnet  is 
in  the  same  horizontal  plane  with  long  magnet.  Point  on  the  middle 
division  of  the  scale  of  the  suspended  magnet,  checking  its  swing  to 
about  two  divisions  of  the  scale,  and  read  the  horizontal  circle. 
Move  the  long  magnet  out  to  the  longer  distance  and  again  point  on 
the  middle  division  of  the  scale  of  the  suspended  magnet  and  read  the 
horizontal  circle.  Turn  the  long  magnet  end  for  end  and  repeat  the 
pointing  and  reading;  then  move  it  up  to  the  shorter  distance  and 
make  a  fourth  pointing  and  reading.  Remove  the  thermometer  from 
the  east  bar,  read  it,  and  place  it  inside  the  west  bar.  Place  the  long 
magnet  with  north  end  west  at  the  shorter  distance  on  the  west  bar 
and  the  torsion  weight  on  the  east  bar.  The  subsequent  procedure 
is  the  same  as  for  long  magnet  east.  Read  the  thermometer  at  the 
close.  The  observer  should  bear  in  mind  that  it  is  the  temperature 
of  the  long  magnet  which  is  required  both  in  oscillations  and  in  deflec- 
tions, and  he  should  endeavor  to  place  the  thermometer  so  that  it 
will  be  of  the  same  temperature  as  the  magnet.  If  the  temperature  is 
changing  rapidly  or  if  it  is  materially  different  on  the  two  bars,  more 
readings  should  be  taken  than  are  specified  above. 

A  second  set  of  deflections  should  follow  immediately  after  the  first, 
but  with  both  magnets  inverted  and  reversing  the  order  of  the  posi- 
tions of  the  long  magnet.  At  its  close,  return  the  short  magnet, 
deflection  bars,  and  torsion  weight  to  the  magnetometer  case,  suspend 
the  long  magnet  inverted,  return  the  thermometer  to  its  case  and  to 
the  hole  in  the  magnet  house,  and  make  a  second  set  of  oscillations. 

A  second  set  of  declination  observations  usually  follows,  but  the 
horizontal  circle  should  first  be  shifted  so  as  to  bring  the  readings  on 
a  different  part  of  the  graduation. 


DETERMINATION  OF  THE  HORIZONTAL  INTENSITY. 


77 


Form  41. 

HORIZONTAL  INTENSITY. 

Station,  Smyrna  Mills,  Me. 

Magnetometer  No.  20.    Magnet  20  L. 

Chronometer,  245,  daily  rate  losing  0».2  on  mean  time. 


OSCILLATIONS. 

Date,  Friday,  August  5,  1910. 
Observer,  H.  E.  McComb. 


Number  of 
oscillations. 

Chronometer 
time. 

Temp. 

t/ 

Extreme  scale 
readings. 

Circle  reading. 

ft.  TO. 

s. 

o 

d. 

d. 

0           ,          „ 

0 

9  38  14.  4 

27.7 

12.0 

48.0 

226  45  20 

5 
10 
15 
20 
25 
30 
35 

38  42.  9 
39  11.6 
39  40.1 
40  08.  6 
40  37.2 
41  05.7 
41  34.3 

28.1 

14.0 

45.5 

46  45  40 

226  45  30 

Time  of 
50  oscillations. 

TO.      S. 

50 

9  42  59.  9 

4    45.5 

55 

43  28.5 

45.6 

60 

43  56.9 

45.3 

65 

4425.7 

45.6 

70 

44  54.  0 

45.4 

75 

45  22.  7 

. 

45.5 

80 

45  51.  0 

45.3 

85 

46  19.7 

28.7 

15.  7                43.  5 

45.4 

Means. 

28.17 

13.  90              45.  67 

4    45.45 

Formula:  MH=n2  E 

[/     ^400    \   / 
T2  I       '                 1  1    1  -i-f 

-*')?)  (H 

H 

)] 

"IT 

Torsion  observations. 

Time  of  loscil. 
Corr'n  for  rate  * 

T 

Log  T* 

5.70900 

+        1 

Torsion 
circle. 

Scale. 

Mean.   Diff's. 

5.  70901 

0 

d. 

d. 

d.          d. 

1.  51312 

80 
170 
350 
80 

28.8 
27.2 
29.5 
28.9 

30.0 
30.0 
30.7 
30.0 

29.40  ! 
28.60  !  0.80   (<-*')  =  -  0.°87 
30.10     1.50 
29.45     0.65 

(,5400^ft/ 
«    [l  +  (t-t')q] 

••  0+4) 

"  Divisor 

"    7T2    K 

"     MH 

12 
-  18 
123 

1.  51429 

Mean 

ft=  0*74=1  '.48 

3.  24733 

One  division  of  scale=2'.00. 

1.  73304 

Plus  for  losing  rate  and  minus  for  gaining  rate.' 


78 


DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 


Form  39. 

HORIZONTAL  INTENSITY. 

Station,  Smyrna  Mills,  Me. 
Magnetometer,  No.  20. 
Long  magnet  deflecting. 


DEFLECTIONS. 

Date,  Friday,  August  5, 1910. 
Observer,  H.  E.  McComb. 
Short  magnet  suspended. 


Circle  readings. 

Mag-  North 
net.     end.               I.  Distance  r=30  cm. 

II.  Distance  r-40  cm. 

No.           A.             B.       Mean. 

No. 

A.              B.        Mean. 

• 

2 
3 

|E.           1          236  57  10       57  20       57  15 
«        W.          4         216  04  40       04  50      04  45 

230  52  20       52  30     52  25 
222  07  50       08  00     07  55 

2tt                                 20  52  30 

8  4430 

1       W.         5         216  17  40      17  50       17  45 
£       E.          8         236383038503840 

6 
7 

222  11  10       11  20     11  15 
230  45  20       45  30     45  25 

2tt                                20  20  55 

834  10 

Fondas:  |-  £(.+£fS)  (.-«£)  Jsi-.-als 

I.                                   II. 

2  u  (mean)                       20  36  42          8  39  20 

u                                       10  18  21          4  19  40 

1 
. 

Value  of  log  MH  from  oscillations: 

h.   m. 
Began  at              9    55                   Temp.  26.  6 

Ended  at            10    13                       "       28.0 

Set. 

I. 

II. 

log  C 
"  Sin  a 

5.86935 
9.25262 

5.  49414 
8.87773 

a     — 
M 

8.  61673 

8.61641 

"     MB 
H 

1.73304 
9.17488 

1.73304 
9.  17472 

H 

.14958 

.14953 

log  M 
Red'n 
20° 
log  Mt 

to 

i 

2.55816 
+  152 

2.55968 

2.55832 
+  152 

2.55984 

Mean              10    04                          /=  27.  3 
Chron.  corr'n         +27 

L.  M.  T.              10    31 

Mean 

2.55976 

COMPUTATION. 


The  computation  involves  simply  the  substitution  of  the  observed 
quantities  and  the  instrumental  constants  in  the  formulas  and  requires 
little  explanation.  The  observer  is  supplied  with  a  table  of  constants 
which  gives,  for  the  magnetometer  he  is  to  use,  the  results  of  the  special 
observations  made  for  determining  the  scale  value,  moment  of  inertia, 


DETERMINATION  OF  THE  HORIZONTAL  INTENSITY. 


79 


temperature  coefficient,  distribution  coefficients,  and  induction  coeffi- 
cient of  the  long  magnet  and  the  deflection  distances,  and  the  com- 
bination of  the  last  four  (log  C)  which  enters  into  the  deflection  formula. 
For  the  magnetometer  used  in  the  example,  this  table  was  as  follows : 

Constants  of  magnetometer  No.  20. 
One  division  of  scale  of  long  magnet  =  2'. 00. 

Deflection  distances.  log  C  at  20°  C. 

cm. 

29.9874  log  =1.47694  5.86953 

40.0054  1.60212  5.49432 

For  an  increase  of  1°  C.  in  temperature  log  C  must  be  diminished 
by  0.000025.     (See  Table  VII.) 

Temperature  coefficient  #  =  0.00048  for  1°  C.;  log  (1  +  q)  =  0.000208 
Distribution  coefficient  P=  —0.955 


Induction  factor  JJL 

TT 

When  log  ^r> 


6.81 
6.50 

6.55 
6.60 
6.65 
6.70 
6.75 
6.80 


log 


log// =  0.833 

0.00093 

105 
118 
132 
148 
166 
186 


Moment  of  inertia  K 


Temp. 
0°C. 
10 
20 
30 
40 


log 

3.  24703 
713 
724 
735 
745 


Computing  the  elapsed  times  between  oscillations  0  and  50,  5  and 
55,  10  and  60,  etc.,  gives  8  independent  values  of  the  time  of  50 
oscillations.  The  mean  of  these  8  quantities  divided  by  50  is  the 
time  of  1  oscillation,  T,  which  must,  however,  be  corrected  for 
the  rate  of  the  chronometer.  The  loss  in  24  hours  being  08.2,  the 
loss  in  5s. 7  would  be  0.2x5.7-^86400,  or,  since  the  correction  to  the 
fifth  decimal  place  is  desired,  0.2x5.7x1.16.  Table  V  gives  the 
value  of  this  correction  for  different  rates  and  different  times  of 
oscillation.  The  formula  for  MH  is  arranged  for  logarithmic  com- 
putation, so  that  log  Jffl  =  log  7i*K-[\og  T2  +  log(  g^°i.  ^ 

\  o4UU— fl  / 

+  log  (  1  +  (t  —  t'}  q)  +  log  (  1  +  fj. ^rr  1   .     As  the  second  and  third  fac- 
tors of  the  divisor  never  differ  much  from  unity,  their  logarithms 


80  DIRECTIONS  FOR   MAGNETIC    MEASUREMENTS. 

are  always  nearly  zero  and  it  may  be  assumed  without  appreciable 
error  that  the  logarithm  varies  directly  as  the  variable  part  of  the 
factor,  i.  e.  :  , 

log  [5400  ^-  (5400  -Ji)]  =  h  log  [5400  -s-  (5400  -  1)] 
log  [1  +  (*-*')  q]  =  (t-t')  log  (l+q) 

Now  log  (5400-^5399)  =  0.00008.  Hence  the  torsion  correction,  ex- 
pressed in  units  of  the  fifth  decimal  place  of  the  logarithm  is  found 
by  multiplying  by  8  the  effect  of  90°  of  torsion.  In  the  example, 
7i=l'.48  and  the  corrective  term  is  therefore  .00012.  The  value  of 
this  factor  may  also  be  obtained  from  Table  VI.  In  the  example 
*-*'  =  27.030-28.°17  =  -0.°87.  From  the  table  of  constants  for  this 
instrument  it  will  be  seen  that 


log  (l  +  q)  =  0.000208 
hence  log  [l  +  (t-t')  q]  =  .  000208  (-0.87)=  -.00018 

A  table  may  readily  be  prepared  for  a  particular  instrument  giving 
the  value  of  this  factor  for  different  values  of  (t  —  t').     The  value  of 

7T\ 

be  found  in  the  table  of  constants  for  different 


( 


H  H 

values  of  log  ,,,  and  the  value  of  log  ,,  is  obtained  from  the  com- 


putation of  deflections.  The  value  of  log  T^K  for  the  temperature 
of  the  oscillations  is  found  by  interpolation  from  the  table  of  constants. 
When  the  computation  has  been  completed,  the  value  of  log  M  H 
is  carried  forward  to  the  deflection  form. 

The  differences  between  the  pairs  of  circle  readings  at  the  two 
distances  give  two  values  of  2  u,  double  the  deflection  angle,  for  each 
distance,  from  which  the  values  of  u  are  obtained.  The  values  of 
log  C  for  the  two  deflection  distances  are  given  in  the  table  of  con- 
stants for  the  temperature  20°  C.  In  the  example  the  deflections 
were  made  at  a  temperature  27.°30  C.  Hence  the  tabular  values  of 
log<7  must  be  decreased  by  0.000025  (27.30  -20)  =  0.00018.  The 

TJ 

values  of  log  ^  are  then  obtained  by  subtracting  log  sin  u  from  log  C. 

In  good  work  the  two  values  seldom  differ  by  more  than  0.00050. 
Should  they  differ  by  as  much  as  0.00100  the  computation  should 
be  revised  and  if  no  mistake  is  found  the  observations  should  be 
repeated. 

TJ 

The  computation  of  H  and  log  M  from  log  H  M  and  log  ^  follows. 

The  resulting  values  of  log  M  are  for  the  temperature  of  deflections, 
27.°30.  The  magnetic  moment  of  a  magnet  varies  with  temperature, 
*,s  we  have  seen,  and  in  order  to  compare  the  values  obtained  at 


DETERMINATION    OF   THE  TOTAL  INTENSITY.  81 

different  times  it  is  necessary  to  reduce  all  results  to  the  same  tem- 
perature. 20°  centigrade  has  been  adopted  as  a  standard  and  all 
values  of  log  M  are  reduced  to  that  temperature.  For  practical  pur- 
poses this  may  be  done  by  means  of  the  formula 

log  M20  =  log  M+  (t  -  20°)  log  (1  +  q) 

In  this  case      (£-20°)  =  7.°3      and     log  (1  +q)  =  0.000208. 
Hence  the  correction  to  be  applied  to  log  M  is  +0.00152. 

Experience  has  shown  that  when  a  magnet  is  first  magnetized  its 
magnetic  moment  decreases  quite  rapidly.  The  rate  of  loss  of  mag- 
netism gradually  diminishes .  and  after  a  few  years  becomes  very 
small.  A  comparison  of  the  values  of  log  M2Q  obtained  at  different 
times  in  the  course  of  a  season's  work  is  therefore  valuable  for  several 
reasons.  (1)  It  furnishes  a  test  of  the  accuracy  of  the  horizontal 
intensity  determinations  and  sometimes  leads  to  the  detection  of 
errors  of  observation  or  computation.  (2)  It  furnishes  the  means  of 
correcting  the  adopted  value  of  temperature  coefficient  if  there  is 
considerable  variation  in  temperature  involved  in  the  series  of 
observations.  (3)  An  accident  to  the  magnet,  such  as  a  fall,  or 
improper  packing  for  transportation,  will  usually  be  revealed  by  a 
sudden  decrease  in  log  M20. 

DETERMINATION  OF  THE  TOTAL  INTENSITY. 

The  determination  of  total  intensity  with  a  dip  circle  by  Lloyd's 
method  involves  two  kinds  of  observations:  Dip  with  loaded  needle, 
and  deflections.  As  the  accuracy  of  the  method  depends  upon  the 
constancy  of  the  condition  of  the  needles  between  the  time  of  stand- 
ardization and  the  time  of  observation,  every  care  must  be  taken  to 
secure  that  constancy.  The  needles  must  never  be  remagnetized 
and  must  be  kept  from  close  proximity  to  disturbing  influences. 
The  weight  used  in  the  standardization  observations  should  be  left 
in  place  in  the  needle  and  any  possibility  of  bending  avoided.  When 
the  standardization  observations  are  made,  that  weight  should  be 
selected  which  will  be  best  suited  to  the  region  in  which  the  instru- 
ment is  to  be  used.  The  weight  should  be  in  the  south  end  for 
places  north  of  the  magnetic  equator  and  in  the  north  end  for  places 
south  of  the  magnetic  equator,  so  that  its  effect  will  be  to  diminish 
the  true  dip.  In  the  formula  involved,  F=  C  V  cos  /'  esc  u  esc  u' f 
lf  is  the  dip  with  loaded  needle,  u  is  the  angle  of  deflection,  and 
u'  =  1—1' .  The  effect  on  the  result  of  an  error  in  an  observed  value 
of'/'  will  tend  to  diminish  as  I'  approaches  zero  and  uf  approaches 
90°.  The  best  approximation  to  these  limits  is  usually  secured  by 
using  a  weight  sufficient  to  cause  the  loaded  end  of  the  needle  to 
77213—11 6 


82  DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 

dip  by  a  small  amount,  so  that  /'  differs  from  zero  by  about  the 
same  amount  that  u'  differs  from  90°. 

If  the  season's  work  covers  such  a  large  range  of  dip  that  the  weight 
used  during  standardization  can  not  be  used  throughout,  or  if  for 
some  other  reason  a  change  in  the  weight  becomes  necessary,  the 
change  should  be  made,  if  possible,  at  a  place  where  observations  can 
be  made  before  the  change  as  well  as  after. 

The  remarks  regarding  care  and  cleaning  of  needles  and  agates  and 
adjustment  of  the  dip  circle  made  in  connection  with  determination 
of  the  dip  apply  with  equal  force  here.  The  instrument  having  been 
leveled  and  placed  in  the  magnetic  meridian,  the  observations  of  dip 
with  loaded  needle  follow  in  each  of  the  four  positions:  Circle  east, 
needle  face  east;  circle  west,  needle  face  west;  circle  west,  needle  face 
east;  circle  east,  needle  face  west,  in  the  same  manner  as  for  regular 
dip  observations.  If  the  south  end  is  below  the  horizon  the  dip  is 
regarded  as  negative.  The  loaded  needle  is  then  fastened  in  the  place 
provided  between  the  reading  microscopes,  "face"  out,  and  covered 
by  the  brass  shield.  The  other  (lighter)  intensity  needle  is  placed  on 
the  lifter  face  east  and  lowered  on  to  the  agate  supports.  As  the 
microscopes  are  turned  in  order  to  make  a  pointing  on  the  suspended 
needle,  carrying  with  them  the  deflecting  needle,  it  will  be  found  that 
there  are  two  positions  in  which  the  suspended  needle  may  be  pointed 
upon  by  the  microscopes,  in  one  of  which  it  is  deflected  toward  the  ver- 
tical and  in  the  other  away  from  the  vertical.  The  microscope  which 
in  one  case  points  on  the  north  end  of  the  needle  will  in  the  other  case 
point  on  the  south  end.  The  microscopes  are  considered  direct  (D) 
when  the  south  (upper)  end  of  the  suspended  needle  is  deflected 
toward  the  right  and  reversed  (R)  when  it  is  deflected  toward  the 
left.  The  angular  difference  between  the  two  positions  of  the  needle 
is  2u,  twice  the  angle  of  deflection.  It  may  happen  that  the  sus- 
pended needle  will  be  deflected  out  of  one  quadrant  into  the  adjoin- 
ing one.  In  a  dip  circle  where  the  vertical  circle  is  graduated  in 
quadrants  from  0°  in  the  horizon  to  90°  at  the  top  and  bottom,  this 
fact  must  be  noted  in  the  record  in  order  that  the  deflection  angle 
may  be  computed  correctly.  Thus,  for  a  dip  of  70°  and  a  deflection 
angle  of  30°  the  circle  readings  would  be  40°  in  the  same  quadrant 
and  80°  in  the  next. 

Deflection  observations  are  made  with  microscopes  D  and  li  in 
each  of  the  four  positions:  Circle  east,  needle  face  east;  circle  west, 
needle  face  west;  circle  west,  needle  face  east;  circle  east,  needle  face 
west. 

A  second  set  of  dip  with  loaded  needle,  similar  to  the  first,  is  then 
made.  In  the  intensity  observations,  as  in  regular  dip,  two  point- 
ings on  each  end  of  the  needle  are  to  be  made  in  each  position,  the 
needle  being  lifted  between. 


DETERMINATION    OF   THE  TOTAL  INTENSITY.  83 

In  the  Lloyd-Creak  form  of  dip  circle  the  needle  is  supported  in 
agate  cups,  and  before  a  reading  is  taken  the  needle  must  be  jarred 
to  a  position  of  equilibrium  by  rubbing  or  tapping  a  metal  point  on 
top  of  the  instrument  with  an  ivory  scraper. 

A  value  of  dip  may  be  obtained  from  the  deflection  observations, 
since  the  suspended  needle  is  deflected  by  approximately  equal 
amounts  in  opposite  directions  from  its  undeflected  position. 

A  sample  set  of  observations  and  computation  is  given  below. 
When  the  vertical  circle  is  graduated  from  zero  at  the  sides  to  90°  at 
the  top  and  bottom  and  the  needle  lies  in  the  same  quadrant  for  both 
positions  of  the  microscopes,  direct  and  reversed,  half  the  difference 
of  the  two  circle  readings  gives  the  deflection  angle  and  half  their 
sum  gives  the  dip.  When  the  needle  is  in  one  quadrant  for  micro- 
scopes direct  and  the  adjacent  one  for  microscopes  reversed, 

and          /_90°-- 


When  the  vertical  circle  is  graduated  continuously  from  0°  to  360°, 
the  readings  with  circle  west  are  to  be  substracted  from  180°  in  taking 
the  means. 

Then  D-R  D  +  R 

u  =  —  2~~         and        1=     2 

For  obtaining  u'  =1—1'  the  best  available  value  of  7  must  be  used. 
This  is  generally  the  mean  of  the  results  with  the  two  regular  dip 
needles,  with  the  instrumental  corrections  applied.  These  corrections 
and  the  value  of  log  C  are  determined  at  some  place  where  the  dip 
and  horizontal  intensity  have  been  accurately  determined  by  other 
means,  and  are  usually  supplied  to  the  observer  from  the  office. 
The  formula  arranged  for  computation  by  logarithms  is: 


i       w—\      n     °£  cos      ~^  °£  csc  u  "^  °&  csc 


As  it  usually  happens  that  the  deflection  angle  is  different  for  the 
two  halves  of  the  deflection  set,  the  form  is  arranged  for  computing 
the  two  halves  separately  and  two  values  of  log  C  are  determined 
to  correspond.  The  form  is  also  arranged  to  compute  the  horizontal 
intensity  from  the  formula  H^  F  cos  7. 


84 


DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 


Form  389. 

TOTAL  INTENSITY. 

Station,  Fernandina,  Fla. 

Dip  circle  No.  35. 

End  of  needle  marked  B  north. 


DIP  WITH  LOADED  NEEDLE. 

Date,  April  14, 1910 
Observer,  S.  S.  Winslow. 
Needle  No.  4.  Weight  No.  6. 

North  end*  up. 


Circle  east.                 Circle  west. 

Circle  west. 

Circle  east. 

Needle  face  east. 

Needle  face  west. 

Needle  face  east. 

Needle  face  west. 

S. 

N. 

S. 

N. 

S. 

N. 

8. 

.     N. 

153  35 
38 

15408 
08 

0           / 

334  02 
05 

333  38 
42 

' 
26  24 
25 

206  27 
30 

25  40 
40 

205  32 
35 

36.5 

40.0            24.5 

28.5 

40.0 

33.5 

08.0 

03.5 

-2621.8                       -2626.5 
-26  24.  2 
Mean  /',  Set  1.  -26° 

-25  36.8 
-25 

04'.  8 

-25  54.  2 
45.5 
!*'-/-/'»  88°  29'.  3 

Circle  east. 

Circle  west. 

Circle  west. 

Circle  east. 

Needle  face  east. 

Needle  face  west. 

Needle  face  east. 

Needle  face  west. 

S. 

N. 

S. 

N. 

S. 

N. 

S. 

N. 

153  28 
25 

333  30 
27 

26  31 
28 

206  25 
25 

25  46 
45 

205  40 
38 

154  10 
08 

334  00 
333  58 

26.5 

28.5 

29.5 

25.0 

45.5 

39.0 

oy.ii 

59.0 

-2632.5                        -2627.2 
-26  29.9 
Mean  /',  Set  2.  -26° 

-2542.2                       -2556.0 
-25  49.  1 
09'.  5                           u'-/-/'=88°  34'.  0 

Chron.  time.    Temp. 
h.    m. 
Beginning                          9    55       20.7 
Ending                            10    21       20.8 

Mean                               10    08       20.75 
Corr'n  on  L.  M.  T.              +23 

Remarks: 

L.  M.  T.                            10    31 
Magnetic  meridian  reads 

84  17 

Note  whether  north  end  is  up  or  down.    Do  not  reverse  polarity. 


DETERMINATION    OF   THE   TOTAL   INTENSITY. 


85 


Form  389. 

TOTAL  INTENSITY  DEFLECTIONS. 

Station,  Fernandina,  Fla.  •  Date,  April  14, 1910. 

Dip  circle  No.  35.    Needle  No.  4  deflecting,  No.  3  suspended. 


Circle  east,  needle  face  east. 

Circle  west,  needle  face  west. 

D.* 

R.* 

R.* 

D.* 

S.                N. 

S.               N. 

S.               N. 

S. 

N. 

274  17          94  21 
15                25 

01                           01 

211  30           31  33 

28                30 

0           /                            Of 

266  58           87  00 
55          86  58 

0           1 

329  22 
23 

149  23 
23 

16.  0            23.  0 

29.  0             31.  5 

56.  5            59.  0 

22.5 

23.0 

94  19.5 
125  49.  7 
62  54.  9 
7  =  62  22.  3 

31  30.2 
62  49.  3 
31  24.6 

93  02.  2 
62  25.  0 
31  12.5 
u  =  31  18.  6 

30  37.  2 
123  39.  4 
61  49.7 

Circle  west,  needle  face  east. 

Circle  east,  needle  face  west. 

D. 

R. 

R. 

D. 

S.               N. 

S.               N. 

S.               N. 

S. 

N. 

210  30          30  38 
28                40 

273  10 
15 

93  29 
30 

329  02        149  10 
03                10 

265  24           85  36 
27                32 

02.  5             10.  0 

25.  5             34.  0 

29.  0            39.  0 

12.5 

29.5 

30  53.  8 
125  24.0 
62  42.  0 
7  =  62  19.  8 

94  30.  2 
63  36.  4 
31  48.2 

30  34.  0 
62  47.  0 
31  23.5 
u  =  31  35.  9 

93 
123 
61 

21.0 
55.0 
57.5 

Chron.  time.    Temp. 

h.    m. 
Beginning                          10    05       21.0 
Ending                                10    20       20.8 

Computation  of  F  and 

77. 

log  cos  7'                    9.  95336  ! 
"  cscw                     0.28427 
"  cscu'                   0.00015 

9.  95307 
0.28070 
0.00014 

Mean 
Corr'n  on  L.  M.  T. 

L.  M.  T. 

10    12        20.9 
+23 

10    35 

Sum                           0.  23778 
Half  sum                   0.11889 
log  C                          9.62333 

0.  23391 
0.  11696 
9.  62497 

"    F                          9.  74222  ! 

9.  74193 

7  from  deflections                       62    21.  0 
7  from   regular  dipJNo.  1        62    22.  3 
needles                     (No.  2         62    26.7 

Mean                         9.  74208    F=  .  55218 
log  cos  7                     9.  66574 

"    77                           9.40782    77=.  25575 

*  If  the  vertical  circle  is  graduated  in  quadrants,  note  whether  the  upper  (south) 
end  of  the  suspended  needle  is  north  or  south  of  the  vertical. 


DIRECTIONS  FOR  OBSERVATIONS  AT  SEA. 
INTRODUCTION. 

The  instruments  and  methods  employed  for  determining  the 
magnetic  elements  on  land  require  a  number  of  modifications  for 
observations  on  board  ship.  On  account  of  the  instability  of  the 
ship  as  an  observing  platform,  a  magnetometer  with  fiber  suspension 
can  not  be  used  and  in  the  dip  circle  agate  cups  take  the  place  of 
agate  knife  edges.  The  instruments  must  be  mounted  in  gimbals 
in  order  that  they  may  remain  approximately  level  in  spite  of  the 
motion  of  the  ship.  It  is  usual  to  determine  the  magnetic  declination 
by  means  of  the  standard  compass  and  an  azimuth  circle,  and  the  dip 
and  total  intensity  by  means  of  a  Lloyd-Creak  dip  circle. 

On  account  of  the  disturbing  effect  of  the  iron  and  steel  which 
enter  more  and  more  into  the  construction  of  modern  ships,  the 
direct  results  of  magnetic  observations  on  shipboard  are  different 
for  different  headings  of  the  ship,  since  they  represent  the  combined 
effect  of  the  earth's  magnetism  and  the  ship's  magnetism,  and  means 
must  be  provided  to  separate  the  resultant  into  its  component  parts. 
It  is  customary,  therefore,  to  make  observations  on  8  or  16  equi- 
distant headings  while  steaming  in  a  circle,  first  in  one  direction  and 
then  in  the  other.  As  a  complete  determination  of  dip  and  intensity 
on  each  heading  of  the  forward  and  back  swings  would  consume  too 
much  time,  the  practice  has  been  adopted  by  the  Coast  and  Geodetic 
Survey  of  observing  deflections  alone  while  swinging  ship  in  one  direc- 
tion and  loaded  dip  alone  while  swinging  in  the  opposite  direction. 
In  addition  to  the  total  intensity  derived  from  the  combination  of 
these  observations,  a  value  of  dip  on  each  heading  results  from  the 
deflection  observations. 

The  determination  of  declination,  dip,  and  total  intensity  at  sea 
requires,  first,  that  observations  be  made  with  the  dip  circle  at  a 
base  station  on  shore  at  the  beginning  and  end  of  the  cruise,  to 
determine  the  intensity  constant  for  the  particular  weight  used  at 
sea  and  the  correction  to  the  dip  as  derived  from  the  deflection  ob- 
servations; and,  second,  that  the  ship  be  swung  at  the  beginning  and 
end  of  the  cruise  (and,  if  possible,  in  the  highest  and  lowest  latitudes 
reached)  at  a  place  near  shore  where  the  declination,  dip,  and  in- 
tensity are  known  with  reasonable  accuracy  from  shore  observations, 
in  order  to  determine  the  deviations  of  the  standard  compass  and  of 
dip  and  intensity  at  the  dip  circle  position. 

87 


88  DIRECTIONS   FOR  MAGNETIC   MEASUREMENTS. 

For  the  general  theory  of  the  analysis  of  a  ship's  magnetism  the 
reader  is  referred  to  the  various  publications  of  the  hydrographic 
offices  of  different  nations,  at  least  one  of  which  is  to  be  found  on 
almost  every  ship.  (E.  g.  "Practical  Problems  and  the  Compensa- 
tion of  the  Compass  in  the  United  States  Navy;"  (British)  "Admiralty 
Manual  for  the  Deviations  of  the  Compass;"  "Der  Kompass  an  Bord," 
issued  by  the  Deutsche  Seewarte,  etc.) 

DECLINATION. 

The  amount  by  which  the  compass  needle  points  east  or  west  of 
true  north  is  called  the  compass  error. 

The  amount  by  which  the  compass  needle  points  east  or  west  of 
magnetic  north  is  called  the  deviation.  In  each  case  east  is*  considered 
positive  and  west  negative.  As  the  angle  between  the  true  meridian 
and  the  magnetic  meridian  is  the  magnetic  declination,  it  follows 
that: 

Compass  error  —  Decimation  =  Deviation . 

Hence  for  the  determination  of  the  declination  on  board  ship 
it  is  necessary  to  know  the  compass  error  and  the  deviation.  The 
deviation  may  be  represented  approximately  by  an  equation  of  the 
form 

Deviation  =  A  +B  sin  £  +  C  cos  £  +  D  sin  2£  +  E  cos  2£ 

in  which  £  is  the  magnetic  heading  of  the  ship,  counted  from  north 
around  by  east.  The  second  member  of  this  equation  may  be  divided 
into  three  parts:  A,  which  is  constant  for  all  headings;  (B  sin  £  +  C 
cos  £),  called  the  semicircular  deviation,  the  values  on  two  headings 
180°  apart  being  equal  but  of  opposite  sign;  (D  sin  2£  +  E'cos  2£), 
called  the  quadrantal  deviation,  the  values  on  two  headings  90°  apart 
being  equal  but  of  opposite  sign.  In  theory,  the  determination  of 
the  deviations  on  any  five  headings  will  give  five  equations  from  which 
to  compute  the  five  coefficients  A,  B,  C}  D,  E.  In  practice,  however, 
it  is  found  that  satisfactory  results  can  not  be  obtained  unless  ob- 
servations are  made  on  a  greater  number  of  headings  properly  dis- 
tributed. It  is  apparent  that  when  observations  are  made  on  8  or  16 
equidistant  headings,  the  mean  of  the  deviations  will  be  A,  the 
constant  part  of  the  deviation,  and  the  computation  of  the  other 
coefficients  will  be  much  simplified.  For  observations  made  in  this 
way  near  shore  where  the  declination  is  known; 

Mean    compass   error  —  Declination  =  A 
and  for  observations  at  sea  when  A  has  been  determined: 
Mean  compass  error  —  A  =  Declination. 


DECLINATION.  89 

From  this  it  will  be  seen  that  when  observations  are  made  on  a  mul- 
tiple of  four  equidistant  headings  it  is  not  necessary  to  compute  the 
coefficients  B,  C,  D,  E  in  order  to  determine  the  declination,  but  in- 
asmuch as  the  deviations  on  all  headings  are  required  for  purposes 
of  navigation,  and  as  observations  are  sometimes  made  on  only  two 
or  three  headings,  it  is  important  to  determine  B,  C,  D,  E  in  order 
that  the  deviation  on  any  desired  heading  may  be  computed. 

In  the  case  of  observations  on  16  equidistant  headings,  there  will 
be  16  observation  equations  from  which  to  compute  the  four  co- 
efficients by  the  method  of  least  squares.  In  the  formation  of  the 
normal  equations  the  observation  equations  may  be  combined  in 
such  a  way  as  to  eliminate  the  constant  term  A  and  to  leave  only  a 
single  unknown  in  each  normal  equation,  as  shown  in  the  sample 
computation  given  later  on.  As  the  declination  is  not  known  at  sea 
and  the  final  value  of  A  is  not  determined  until  the  end  of  the  season's 
work,  it  is  usually  more  convenient  to  make  the  analysis  of  that 
part  of  the  deviations  which  does  not  involve  A. 

Since 

Compass  error  —  Declination  =  Deviation 

and  Mean  compass  error  —  Declination  =  A 

Compass  error  —  Mean  compass  error  =  Deviation  —  A 

For  want  of  a  better  term  this  part  of  the  deviation  has  been  called 
"star  deviation"  and  designated  by  an  asterisk  after  the  word, 
deviation*. 

Deviation*  =  Deviation  -  A  =  B  sin  £  +  C  cos  r  +D  sin  2£  +  E  cos  2£. 

The  compass  error  is  usually  determined  in  one  of  three  ways: 
(1)  By  observations  of  the  sun;  (2)  by  reciprocal  bearings  with  a 
shore  station;  (3)  by  observing  on  a  range  of  which  the  true  bearing 
is  known. 

(1)  The  compass  bearing  of  the  sun  is  observed  by  means  of  an 
azimuth  circle,  and  the  true  bearing  is  computed  from  the  latitude 
of  the  place  and  the  local  mean  time  of  observation.     This  requires, 
in  addition  to  the  latitude,  a  knowledge  of  the  longitude  and  the  cor- 
rection of  the  chronometer  on  standard  time.     The  computation  is 
very  much  simplified  by  the  use  of  United  States  Hydrographic 
Publication  No.  71,  or  similar  azimuth  tables. 

(2)  For  observations  near  shore  it  is  sometimes  more  convenient  to 
make  use  of  the  method  of  reciprocal  bearings.     An  observer  on  shore 
measures  the  angle  between  the  ship's  binnacle  and  a  reference  mark, 
at  the  same  moment  that  the  observer  on  the  ship  measures  the  com- 
pass bearing  of  the  shore  station.     If  the  true  bearing  of  the  reference 


90 


DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 


mark  from  the  shore  station  is  known,  the  true  bearing  of  the  shore 
station  from  the  ship  at  the  time  of  the  compass  observation  may  be 
computed.  An  older  form  of  this  method,  and  one  wliich  may  be 
used  when  azimuth  observations  are  impossible,  is  to  mount  a  com- 
pass on  shore  and  observe  the  compass  bearing  of  the  ship,  the  dif- 
ference of  the  reciprocal  bearings  being  the  deviation  for  that  particu- 
lar heading,  provided  the  shore  station  is  free  of  local  disturbance  and 
the  compass  free  of  index  error. 

(3)  In  some  harbors  the  true  bearings  of  well  defined  range  lines 
have  been  computed  for  the  convenience  of  navigators  and  the  com- 
pass error  may  be  determined  by  observing  the  compass  bearing  of  one 
of  these  ranges. 

The  forms  of  record  and  computation  are  shown  in  the  following 
example.  In  this  case  the  compass  bearing  of  the  sun  was  observed 
on  16  equidistant  headings  while  swinging  first  with  starboard  helm 
and  then  with  port  helm,  but  only  the  starboard  observations  are 
reproduced. 


Form  364. 


OBSERVATION  OP  COMPASS  DEVIATIONS. 


Steamer.  Sache. 

Date,  July  10, 1909. 

Weather,  clear.    Sea,  choppy.    Wind,  SSW. 

Ship  swung  with  starboard  helm. 


Standard  compass  Xo.  30367. 
Observer,  W.  C.  Hodgkins. 


Ship's  head 
by  standard 
compass. 

Time  by 
hack  watch 
No.  141. 

Sun's  bearing 
by  standard 
compass. 

Remarks. 

wsw. 

ft.  m.  s. 
5  49  40 

0        , 

N.  70  50  W. 

0         1 

Latitude                                     38  20 

sw. 

52  50               70  30 

Longitude                                  76  22.3 

SSW. 

55  50               7000 

s. 

SSE. 
SE. 

58  10 
59  50 
6  0205 

7000 
70  05 
69  10 

Chronometer  comparison: 

ft.  m.  *. 

ESE. 

05  42 

67  30 

Hack  reads 

5  10  19 

E. 

07  30 

66  05 

Chron.  3012 

100800 

ENE. 

10  10 

65  00 

Chron.  corr'n 

+        54 

NE. 

12  30 

6425 

G.  M.  T. 

10  08  54 

NNE. 

15  10 

64  20 

E. 

-    5  05 

N. 

1700 

6600 

G.  A.  T. 

10  03  49 

NNW. 

19  40 

6700 

Longitude 

5  05  29 

NW. 

22  20 

67  30 

Local  A.  T. 

4  58  20 

WNW. 

24  05 

07  35 

Hack  reads 

5  10  19 

W. 

26  10 

67  05 

Hack  correction  on  local 

-  11  59 

apparent  time 

DECLINATION. 


91 


Form  355. 


COMPUTATION  OP  COMPASS  DEVIATIONS. 


Steamer,  Sache. 

Lat.  38°  20'  N.,  long.  76°  22'.3. 

Ship  swung  with  starboard  helm. 


Date,  July  10, 1909. 
Sun's  declination,  22°  14'  N. 


Ship's 
head. 

Local 
apparent 
time. 

Sun's 
bearing  by 
compass. 

Sun's 
azimuth 
from  tables. 

Error  of 
standard 
compass. 

Deviation.* 

h.  m.  s. 

0        / 

0         / 

0       , 

0        / 

N. 

6  05  02 

N,  66  00  W. 

N.  71  31  W. 

5  31  W. 

0  32  W. 

NNE. 

6  03  12 

64  20 

71  46 

7  26 

2  27  W. 

NE. 

6  00  32 

64  25 

72  09 

7  44 

2  45  W. 

ENE. 

5  58  12 

65  00 

72  28                   7  28 

2  29  W. 

E. 

55  32 

66  05 

72  51                   6  46 

1  47  W. 

ESE.                  53  44 

6730 

73  06                   5  36 

0  37  W. 

SE.                   50  07 

69  10 

73  36                   4  26 

0  33  E. 

SSE.                  47  52/ 

70  05 

73  55 

3  50 

1  09  E. 

S.                     46  12 

70  00 

74  09                   4  09 

0  50  E. 

SSW.                 43  52               70  00 

74  28 

4  28 

0  31  E. 

SW.                   40  52        „       70  30 

74  54 

4  24 

0  35  E. 

WSW.                37  42               70  50 

75  20 

4  30 

0  29  E. 

W.                6  14  12               67  05 

70  13 

3  08 

-  51  E. 

WNW.                12  07               67  35 

70  31 

2  56 

203E. 

NW.                  10  22               67  30 

70  46 

3  16 

1  43  E. 

NNW. 

07  42               67  00 

71  08 

4  08 

0  51  E. 

Means 

5  56  42                67  42 

72  41 

4  59  W. 

Magnetic  declination  from  shore  observations,  5°  25'  W. 

92  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

Form  356. 

Steamer,  Bnche. 


ANALYSIS  OF  COMPASS  DEVIATIONS.* 


Date,  July  10, 1909. 


Deviation.* 

(D 

Deviation.* 

(2) 

(3) 

Ship's 

Ship's 

head. 

head. 

1 

Port. 

Starb. 

Mean. 

Port.        Starb. 

Mean. 

(D+(2) 

N. 

-    53 

-    32 

-    42 

S. 

'     i            ' 

+     39         +50 

+    44 

a 

+     2 

NNE. 

-  142 

-  147 

-  144 

ssw. 

-    14         +31 

+      8 

b 

-  136 

NE. 

-  148 

-  165 

-  156 

s\v. 

-     17         +35 

+      9 

c 

-  147 

ENE. 

-  105 

-  149 

-  127 

wsw. 

+    65         +29 

+     47 

d 

-    80 

E. 

-     79 

-  107 

-    93 

w. 

+106         +  111 

+  108 

e 

+      5 

ESE. 

-    17 

-     37 

-     27 

WNW. 

+96         +123 

+  110 

f 

+   .83 

SE. 

+     45 

+     33 

+    39 

NW. 

+  114         +  103 

+  108 

9 

+  147 

SSE. 

+    58 

+     69 

+    64 

NNW. 

+    55         +51 

+    53 

h 

+  117 

Computation  of  B  and  C. 

Computation  of  D  and  E. 

(4) 

(5) 

(6) 

(7) 

(8) 

(9) 

(D-(2) 

(4)X(5) 

(4)X(6) 

From  (3) 

(7)X(8) 

(7)X(9) 

-    86 

.000 

mi 

1.000 

-    86 

a—  e 

-  152 

.383 

-    58 

.924 

-  140 

-     13 

.000 

00 

1.000 

-     13 

-  165 

.707 

-  117 

.707 

-  117 

b-f 

-  174 

.924 

-  161 

.383 

-    67 

-  219 

.707 

- 

155 

.707 

-  155 

-  201 

1.000 

-  201 

.000 

00 

c-g 

-  137 

.924 

-  127 

-  .383 

+    52 

-  294 

1.000 

- 

294 

.000 

00 

-    69 

.707 

-     49 

-  .707 

+     49 

d-h 

+     11 

.383 

+      4 

-  .924 

-    10 

-  197 

.707 

- 

139 

-  .707 

+  139 

8B 

-  709 

8C 

-  319 

8D 



588 

8E 

-     29 

B 

-    89 

C 

-     40 

D 

- 

74 

E 

4 

N.  B.— When  observations  are  made  on  only  8  points,  the  divisors  must  be  changed  from  8  to  4. 


DECLINATION. 

COMPARISON  OF  OBSERVED  AND  COMPUTED  DEVIATIONS.* 
Deviation*=  Deviation— A= B  sin  C+  Ccos  Z.+D  sin  2  Z+E'cos  2  C. 

C  is  the  compass  azimuth  of  the  ship's  heading,  counting  from  north  around  by  east,  south, 
and  west  to  360°. 


93 


Ship's 
head. 

-  89'     '     -  40' 
5  sinC       CcosC 

i 

D  sin  2  C    E  cos  2  C 

Deviation.* 

C-0 

V 

* 

Comp'd. 

Obs'd. 

N. 

00          -  40 

00             -  4 

-    44 

-     42 

-     2 

4 

NNE. 

-  34           -  37 

-  52             -  3 

-  126 

-  144          +  18 

324 

NE. 

-  63           -  28 

-  74                  0 

-  165 

-  156            -     9 

81 

ENE. 

-  82 

-  15 

-  52 

+  3 

-  146 

-  127 

-  19 

361 

E. 

-  89 

00 

00 

+  4 

-    85 

-     93 

i      +    8 

64 

ESE. 

-  82 

+  15 

+  52 

+  3 

-     12 

-     27 

+  15 

225 

SE. 

-  63 

+  28 

+  74 

0 

+     39 

+     39 

0 

0 

SSE. 

-  34 

•    +  37 

+  52 

-  3  i       +52 

+     64 

-  12 

144 

S. 

00 

+  40 

00 

-  4 

+     36 

+     44 

-    8 

64 

ssw. 

+  34 

+  37 

-  52 

-  3 

+     16 

+      8 

+    8 

64 

sw. 

+  63 

+  28 

-  74 

0         +17+9 

+    8 

64 

wsw. 

+  82 

+  15 

-  52 

+  3         +48       +47 

+     1 

1 

w. 

+  89 

00 

00 

+  4         +93       +108 

-  15 

225 

WNW. 

+  82 

-  15 

+  52 

'+  3 

+  122       +  110 

+  12 

144 

NW. 

+  63 

-  28 

+  74 

0 

+  109       +108 

+     1 

1 

NNW. 

+  34 

-  37 

+  52 

-3+46       +53 

-    7 

49 

1  J* 

1815 

Probable  error  of  single  observation,  r=  ±8'. 
For  16  points,  r=  ±0.195  V^-    For  8  points, 

Before  and  after  the  sun  observations  the  observing  timepiece  was 
compared  with  the  standard  chronometer  and  its  correction  on  local 
apparent  time  computed  as  shown.  The  mean  of  the  two  compari- 
sons gave  the  correction  —  1 1 m  58s,  and  this  was  applied  to  the 
recorded  times  of  observation  to  get  the  local  apparent  times  of 
observation  given  in  the  second  column  of  the  form  for  "  Computa- 
tion of  Compass  Deviations." 

Hydrographic  Office  Publication  No.  71  gives  the  sun's  azimuth 
at  10-minute  intervals  between  sunrise  and  sunset  for  each  degree  of 
latitude  from  61°  N.  to  61°  S.  and  for  each  degree  of  declination  of 
the  sun.  As  three  interpolations  are  in  general  required  to  get  a 
desired  azimuth,  it  expedites  the  computation  of  a  series  of  observa- 
tions to  prepare  from  the  azimuth  tables  an  auxiliary  table  with 
which  only  a  single  interpolation  will  be  necessary.  In  the  example 
given  the  observations  extended  from  5h  37m  to  6h  47m  p.  m.,  and 
the  following  table  was  prepared  to  cover  that  period  for  latitude 
38°  20'  X.  and  sun's  decimation  22°  14'  X. 


94 


DIRECTIONS   FOE  MAGNETIC    MEASUREMENTS. 
Azimuth  of  the  Sun  on  July  10,  1909. 


Declination. 
Latitude. 

22°  N. 
38°  N. 

22°  14'  N. 
38°        N. 

22°14'N.     !     22°14'N. 
39°        N.         38°  20' 

Change 
permin. 

h.  m. 

0          / 

0         / 

5  30 

N.  76  30  W. 

N.  76  18  W. 

N.  76  38  W.     N.  76  25  W. 

40 

75  07 

74  55 

75  13                 75  01 

8.4 

50 

73  44 

73  32 

73  48                 73  37 

8.4 

600 

72  20 

7208 

72  23                 72  13 

8.4 

10 

70  56 

70  45 

70  57                 70  49 

8.4 

20 

69  31 

69  20 

69  30                 69  23                      8.  6 

30 

68  06 

6755 

68  02                 67  57 

8.6 

40 

66  39 

66  28 

66  34                 66  30 

8.7 

50 

65  11 

6500 

65  04                 65  01 

8.9 

A  column  has  been  added  containing  the  values  for  latitude  28° 
N.  and  declination  22°  N.  taken  directly  from  the  azimuth  tables. 
A  comparison  of  these  values  with  the  corresponding  ones  in  column  5 
shows  differences  changing  gradually  from  5'  at  the  beginning  to 
10'  at  the  end.  From  this  it  will  be  seen  that  the  desired  azimuths 
may  be  obtained  without  the  aid  of  an  auxiliary  table  if  the  cor- 
rections to  the  table  for  the  nearest  even  degree  of  latitude  and 
declination  be  computed  for  the  beginning  and  end  of  the  series  of 
observations.  As  it  is  the  usual  practice  to  combine  swings  with  port 
and  starboard  helms,  it  will  be  sufficiently  accurate  for  practical  pur- 
poses to  determine  the  correction  for  the  middle  of  each  swing  and 
assume  that  it  is  constant  throughout  the  swing. 

The  difference  between  the  observed  compass  bearing  of  the  sun 
and  its  computed  true  bearing  is  the  error  of  the  compass  for  that 
heading.  By  subtracting  the  mean  compass  error  from  the  error 
for  each  heading  the  corresponding  deviations  *  (star  deviations)  are 
found,  provided  observations  have  been  made  on  each  of  8  or  16 
equidistant  headings.  It  sometimes  happens  that  the  observation 
on  one  heading  is  prevented  by  the  mast  or  funnel  coming  in  line 
with  the  sun.  In  such  case  the  missing  compass  error  must  be  sup- 
plied by  interpolation  before  taking  the  mean.  This  can  usually  be 
done  with  sufficient  accuracy  by  comparison  with  the  swing  in  the 
opposite  direction.  If  the  observations  on  several  headings  have 
been  prevented  by  clouds,  graphical  interpolation  should  be  resorted 
to,  plotting  the  observed  compass  errors  and  drawing  a  smooth  curve 
to  represent  them. 

The  analysis  of  the  compass  deviations  *  requires  little  explana- 
tion, as  the  order  of  computation  is  indicated  by  the  headings  of  the 
form.  For  two  headings  £  and  (180° -f£)  the  observation  equations 
would  be: 


DECLINATION.  95 

Deviation  *  (£)  =  B  sin  £  +  C  cos  £  +  D  sin  2£+E  cos  2£ 


and 

Deviation  *  (180°  +£)  =  -  5  sin  £  -  C  cos  £  +Z>  sin  2£  +  #  cos  2£ 
Hence 

Deviation  *  (£)  -  Deviation*  (180°  +C)  =  ^i  =  2  .£  sin  £  +  2  (7  cos  £ 
and 

Deviation*  (£)  +  Deviation*  (180°  +£)  =  ^2  =  2  D  sin  2£  +  2  #cos  2£ 

It  will  be  seen  that  the  quantities  on  the  same  line  in  columns 
headed  (1)  and  (2)  are  in  each  case  the  deviations  *  for  two  headings 
180°  apart,  and  hence  the  quantities  in  column  (3)  involve  only  the 
factors  D  and  E  (quadrantal  deviation)  and  those  in  column  (4) 
involve  only  B  and  C  (semicircular  deviation). 
From  observation  equations  of  the  form: 

Jx  =  2  B  sin  £  +  2  C  cos  £ 

the  values  of  B  and  C  are  obtained  by  the  method  of  least  squares 
from  the  normal  equations  : 

IA^  sin  £  =  2  B  I  sin2  £  +  2  C  I  sin  £  cos  £ 
I  A±  cos  £  =  2  B  I  sin  £  cos  £  +  2  C  I  cos2  £ 

The  values  of  sin  £  and  cos  £  for  angles  corresponding  to  the  equi- 
distant headings  N,  NNE,  ____  SSE,  are  given  in  columns  (5)  and 
(6)  .  It  will  be  seen  that  I  sin2  £  =  4,  1  sin  £  cos  £  =  0  and  21  cos2  £  =  4. 
Hence  for  the  case  of  observations  on  16  equidistant  headings  the 
normal  equations  become: 

2Ai  sin  £  =  8  B  ZA^  cos  £  =  8  C 

and  the  computation  is  made  in  the  simple  manner  indicated  on  the 
form.  For  observations  on  8  equidistant  headings  only  the  values 
of  sin  £  and  cos  £  given  on  the  first,  third,  fifth,  and  seventh  lines  will 
be  involved  and  the  normal  equations  will  be: 

ZA^  sin  £  =  4  E  ZA^  cos  £  =  4  C 

In  the  publication  of  the  various  Hydrographic  Offices  treating  of 
the  compass  and  its  deviations,  tables  are  given  to  facilitate  the  com- 
putation of  AI  sin  £  and  A^  cos  £,  where  the  deviations  are  expressed 
in  degrees  and  minutes.  For  the  small  deviations  involved  in  obser- 
vations on  the  ships  of  the  Coast  and  Geodetic  Survey  it  will  be 
found  convenient  to  convert  the  deviations*  to  minutes  and  use 
Table  XIII  given  at  the  end  of  this  publication. 

It  has  been  shown  above  that  the  sum  of  the  observation  equa- 
tions for  two  headings  180°  apart  would  be: 

J  =  2  D  sin  2  +  2  E  cos  2 


96  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

For  the  two  headings  90°  from  the  first  two  the  quantities  in  the 
second  member  would  be  the  same,  but  the  signs  would  be  changed. 
The  difference  of  the  two  equations  would  give: 


J3  =  4  D  sin  2£  +  4  E  cos  2£ 

The  values  of  J3  are  given  in  the  column  headed  (7),  obtained  from 
column  (3)  in  the  manner  indicated.  The  corresponding  normal 
equations  are: 

JJ3sin2£  =  8#         and         JJ3  cos  2£  =  8  E 
for  observations  on  16  headings, 
and  I  J3  sin  2£  =  4  D         and         I  J3  cos  2£  =  4  E 

for  observations  on  8  headings.     The  quantities  in  columns  (8)  and 
(9)  are  the  shies  and  cosines  of  0°,  45°,  90°,  and  135°,  respectively. 
The  analysis  of  the  observations  in  the  example  gives: 

Deviation  *=  -89'  sin  £-  40'  cos  £-.74'  sin  2£-4'  cos  2r 

from  which  the  deviation  *  on  any  heading,  £,  can  be  computed.  As 
a  test  of  the  accuracy  of  the  observations  a  comparison  should  be 
made  between  the  deviations  *  derived  from  the  observations  and 
those  computed  from  the  formula.  For  observations  on  16  headings 
the  probable  error  of  a  single  observation  (mean  of  swings)  is  given 
by  the  formula: 

Vlv2 
1(._4  =  0.195^V 

Where  observations  are  made  on  only  8  headings, 


rw 

=  0.6745^  8  —4  =  0.337  V-  '" 


In  the  example  r=  ±8'.     For  observations  under  i'a  vorable  condi- 
tions that  represents  about  an  average  value. 

For  navigational  purposes  the  complete  deviations  are  required. 
They  may  be  obtained  by  adding  the  constant  part  of  the  deviation, 
A,  to  the  deviations.*  As  already  pointed  out,  A  is  determined  from 
swings  near  shore  where  the  declination  is  known  at  least  approxi- 
mately. As  the  declination  where  the  ship  is  swung  is  in  general 
not  exactly  the  same  as  at  the  point  on  shore  where  observations  are 
made,  it  is  desirable  to  combine  the  results  obtained  at  a  number 
of  places  to  get  a  mean  value  of  A.  While  this  constant  part  of  the 
compass  deviation  is  no  doubt  partly  due  to  unsymmetrical  distri- 
bution of  the  ship  magnetism  with  respect  to  the  compass,  the  greater 
part  is  to  be  ascribed  to  imperfections  in  the  compass  and  the  azimuth 
circle,  corresponding  to  an  index  error. 


DIP  AND   TOTAL  INTENSITY.  97 

Since  the  deviation  is  the  resultant  effect  of  the  forces  exerted  on 
the  compass  needle  by  the  ship's  magnetism  and  the  earth's  mag- 
netism, it  follows  that  any  change  in  the  ratio  of  those  two  forces 
will  produce  a  change  in  the  deviation.  The  quadrantal  deviation 
is  due  to  the  magnetism  induced  in  horizontal  soft  iron  and  therefore 
varies  directly  as  H  varies,  and  for  a  particular  heading  the  ratio  of 
the  two  does  not  change  when  the  ship  goes  from  place  to  place. 
Hence  the  coefficients  D  and  E  should  be  constant. 

The  semicircular  deviation  is  due  partly  to  the  subpermanent  mag- 
netism of  the  ship  and  partly  to  induced  magnetism  in  vertical  soft 
iron.  The  former  is  constant,  or  nearly  so,  and  therefore  produces  an 
effect  on  the  compass  needle  which  is  inversely  proportional  to  H. 
The  induced  magnetism  in  vertical  sof^  iron  is  proportional  to  the 
vertical  force  or  H  tan  7,  and  its  effect  on  the  compass  needle  is  there- 
fore proportional  to  tan  7.  As  H  decreases  and  7  increases  in  going 
from  the  magnetic  equator  to  the  magnetic  poles,  it  follows  that  in  the 
northern  hemisphere  B  and  C  should  become  greater  as  the  ship  goes 
farther  north  and  vice  versa. 

DIP  AND  TOTAL  INTENSITY. 

On  several  of  the  ships  of  the  Coast  and  Geodetic  Survey  dip  and 
total  intensity  are  determined  by  means  of  a  Lloyd-Creak  dip  circle 
mounted  on  a  gimbal  stand  as  shown  in  Figure  9.  The  balance  of  the 
instrument  is  secured  by  a  counter-poise  at  the  back,  and  its  stability 
is  regulated  by  a  heavy  ball  threaded  onto  a  rod  extending  below 
the  gimbal  rings.  The  instrument  is  leveled  in  the  same  manner  as 
when  mounted  on  a  tripod  on  land. 

Experience  with  the  original  form  of  Lloyd-Creak  dip  circle  showed 
that  within  30°  or  40°  of  the  magnetic  equator  it  was  impossible  to 
observe  deflections,  as  the  earth's  total  intensity  became  too  small  to 
offer  sufficient  resistance  to  the  force  exerted  by  the  deflecting  needle, 
and  the  suspended  needle  would  not  come  to  rest  at  right  angles  to 
the  deflector.  To  remedy  this  defect  several  dip  circles  of  this  type 
have  been  modified  in  the  instrument  shop  of  the  Coast  and  Geodetic 
Survey  so  as  to  increase  the  distance  between  the  two  needles  when 
making  deflection  observations.  The  loaded  needle,  when  in  use  as  a 
deflector,  is  mounted  in  an  aluminum  case  which  fits  in  a  frame 
between  the  reading  microscopes,  as  shown  in  Figure  9.  The  needle  is 
mounted  to  one  side  of  the  center  of  the  case,  so  that  the  deflections 
may  be  made  at  two  deflection  distances  by  reversing  the  position  of 
the  case  in  its  supporting  frame.  Originally  the  needles  were  7.3  cm. 
apart  during  deflections.  With  the  new  arrangement  the  distances 
are  7.9  and  9.4  cm.,  respectively,  and  it  is  possible  to  observe,  at  least 
at  the  longer  distance,  in  any  part  of  the  globe.  In  the  instrument 
77213—11 7 


98 


DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 


shown  in  the  figure  a  small  telescope  was  added,  so  that  astronomical 
observations  on  land  can  be  made  if  desired. 

Dip  observations  may  be  made  with  the  regular  dip  needles  in  the 
same  manner  and  with  nearly  the  same  facility  as  on  land.  The  only 
difference  is  that  the  ivory  scraper  must  be  used  continuously,  and 
when  the  needle  swings  through  a  large  arc  on  account  of  the  motion 
of  the  ship,  the  extremes  of  the  swing  must  be  read  and  recorded 
instead  of  attempting  to  estimate  the  middle.  As  it  is  usual  to  make 
observations  on  8  or  16  equidistant  headings  in  order  to  eliminate 
the  varying  effect  of  the  ship's  magnetism,  a  complete  determination 
of  dip  and  intensity  on  each  heading  would  require  too  much  time, 


FIG.  9.— Lloyd-Creak  pattern  dip  circle. 

and  the  following  scheme  of  observations  has  been  adopted  with 
satisfactory  results. 

(1)  Deflection  observations  are  made  while  swinging  ship  in  one 
direction  and  dip  with  loaded  needle  while  swinging  in  the  opposite 
direction.     The  combination  of  these  observations  will  give  a  value  of 
total  intensity  for  each  heading,  and  from  each  observation  of  deflec- 
tions a  value  of  dip  may  be  obtained,  as  explained  on  page  83. 

(2)  On  each  heading  observations  are  made  in  only  one  position  of 
needle  and  circle,  so  as  to  require  not  much  more  time  than  the  com- 
pass observations,  which  are  usually  going  on  at  the  same  time.     As 
the  gimbal  stand  is  set  so  that  when  the  horizontal  circle  of  the  dip 
circle  reads  zero  the  needle  swings  in  the  plane  of  the  fore-and-aft  line 


DIP  AND   TOTAL  INTENSITY. 


99 


of  the  ship,  the  instrument  may  be  placed  in  the  magnetic  meridian 
with  sufficient  accuracy  by  means  of  the  heading  of  the  ship  as  shown 
by  the  standard  compass.  For  observations  on  16  headings  the 
arrangement  would  be  as  follows: 


Heading. 

Needle  face. 

Ver.  circle. 

HOT.  circle 
setting. 

N. 

E. 

E. 

36000 

NNE. 

E. 

E. 

337  30 

NE. 

E. 

E. 

315  00 

ENE. 

E. 

E. 

292  30 

E. 

W. 

W. 

90  00 

ESE. 

W. 

W. 

67  30 

SE. 

W. 

W. 

45  00 

SSE. 

w. 

w. 

2230 

S. 

E. 

w. 

36000 

SSW. 

E. 

w. 

337  30 

sw. 

E. 

w. 

315  00 

wsw. 

E. 

w. 

292  30 

w. 

W. 

E. 

90  00 

WNW. 

W. 

E. 

67  30 

NW. 

W. 

E. 

45  00 

NNW. 

w. 

E. 

2230 

(3)  Two  readings  of  each  end  of  the  needle  are  made  for  each 
position.     In  case  the  needle  is  so  nearly  horizontal  that  only  one  end 
can  be  read,  four  readings  are  made  of  that  end. 

(4)  The  times  of  beginning  and  ending  of  observations  for  each 
group    of   four   headings   and   the   corresponding   temperatures   are 
recorded,  also  conditions  of  weather,  sea,  etc. 

The  variation  in  the  values  of  7,  7',  and  u  for  the  four  different 
positions  of  circle  and  needle  can  be  determined  from  the  shore  obser- 
vations, and  the  values  obtained  on  shipboard  should  be  corrected 
accordingly  to  reduce  to  the  mean  of  the  four  positions,  in  case  the 
corrections  amount  to  as  much  as  10 ';  in  any  case  the  values  of  dip 
must  be  corrected  to  reduce  to  the  standard  dip  instrument.  Sample 
observations  of  the  two  classes  and  the  corresponding  computations, 
and  a  summary  of  the  results  of  a  complete  swing,  are  given  below. 


100 


DIRECTIONS   FOE   MAGNETIC    MEASUREMENTS. 


Form  391. 

MAGNETIC  OBSERVATIONS  ON  BOARD  C.  AND  G.  S.  S.  BACHE. 
LOADED  DIP  FOR  TOTAL  INTENSITY. 


Date,  July  10, 1909.    Latitude,  38°  20'.    Longitude,  76°  22'. 
Dip  circle  No.  35.  Needle  No.  4. 


Weight  No.  6. 


Ship's  head  N. 
Hor.  circle  360°. 
Ver.  circle  E. 
Needle  face  E. 

Ship's  head  NNE. 
Hor.  circle  337*°- 
Ver.  circle  E. 
Needle  face  E. 

Ship's  head  NE. 
Hor.  circle  315°. 
Ver.  circle  E. 
Needle  face  E. 

Ship's  head  ENE. 
Hor.  circle  292*  °. 
Ver.  circle  E. 
Needle  face  E. 

S. 

N. 

S. 

N. 

S. 

N. 

8. 

N. 

345  00 
344  10 

164  40 
164  30 

346  20 
34600 

166  00 
166  10 

348  50 
348  10 

168  40 
16830 

350  50 
351  00 

170  30 
170  50 

34435 

16435 

346  10 

16605 

348  30 

68  35 

350  55 

170  40 

/'        -15  25 

-13  52 

-11  28 

-9  12 

Form  390. 

MAGNETIC  OBSERVATIONS  ON  BOARD  C.  AND  G.  S.  S.  BACHE. 

DEFLECTIONS  FOR  TOTAL  INTENSITY  AND  DIP. 

Date,  July  10, 1909.    Latitude,  38°  20'.    Longitude,  76°  22'. 

Dip  circle  No.  35.  Needle  No.  4  deflecting,  No.  3  suspended. 


Ship's  head  NE.         Hor.  circle  315°. 
Ver.  circle  E.              Needle  face  E. 

Ship's  head  NNE.      Hor.  circle  337*°. 
Ver.  circle  E.               Needle  face  E. 

D. 

R. 

R. 

D. 

N. 

S. 

N. 

S. 

N. 

S. 

N. 

S. 

228  40 
30 

48  20 
30 

285  10 
20 

105  20 
20 

287  10 
20 

107  30 
40 

•J_".*  4U 
40 

4950 
50 

228  35 

48  25 

285  15 

105  20 

287  15 

107  35 

229  40 

49  50 

48  30 
153  47.5 
I         76  54 

105  17.5 
56  47.5 
u       28  24 

107  25 
157  10 
/        78  35 

49  45 
57  40 
u       28  50 

DIP   AND   TOTAL  INTENSITY/ 


Form  392. 


COMPUTATION  OF  TOTAL  INTENSITY*. 


From  observations  on  board  C.  and  G.  S.  S.  Bache. 
Formulas:  u'=I—I'       and        F=  cVcos  /'.  cscTwTcsc  u' 


Date,  July  10, 1909. 


Computer,  H.  M.  Armstrong 


Ship's  head. 

N. 

NNE. 

NE. 

ENE. 

0        , 

0        / 

o     / 

0       / 

r 

-15  25 

-13  52 

-11  28 

-  9  12 

u 

29  03 

28  59 

2833 

27  49 

u' 

94  16 

92  04 

87  59 

83  39 

log  cos  /' 

9.  98409 

9.  98715 

9.  99124 

9.  99438 

"  cscw 

0.  31375 

0.31466 

0.32064 

0.  33101 

"  csc  u' 

0.  00121 

0.  00028 

0.  00027 

0.  00267 

Sum 

0.  29905 

0.  30209 

0.31215 

0.  32806 

Half  sum 

0.  14952 

0.  15104 

0.  15608 

0.  16403 

log  C 

9.  62425 

9.62425 

9.62425 

9.62425 

«  p 

9.  77377 

9.  77529 

9.  78033 

9.78828 

F 

.5940 

.5961 

.6030 

.6142 

SUMMARY  OF  RESULTS. 
Steamer  Sache,  July  10, 1909. 


Head. 

7  obs'd. 

/corr'd. 

/' 

u  obs'd. 

u  corr'd. 

u' 

F 

0   / 

0   / 

0   / 

0   / 

o  / 

0   / 

C,  G.  S. 

N. 

79  14 

78  51 

-15  25 

28  54 

29  03 

94  16 

0.  5940 

NNE. 

78  35 

78  12 

-13  52 

28  50 

28  59 

92  04 

.5961 

NE. 

76  54 

76  31 

-11  28 

28  24 

28  33 

87  59 

.6030 

ENE. 

74  50 

74  27 

-  9  12 

27  40 

27  49 

83  39 

.6142 

E. 

71  01 

71  42 

-  5  20 

27  24 

27  32 

77  02 

.6258 

ESE. 

68  11 

68  52 

-  2  42 

26  19 

26  27 

71  32 

.6473 

SE. 

65  52 

66  33 

-  0  58 

25  28 

25  36 

67  31 

.6662 

SSE. 

64  21 

65  02 

0  00 

25  04 

25  12 

65  02 

.6776 

S. 

64  48 

64  29 

+  0  18 

25  00 

2450 

64  11 

.6846 

SSW. 

65  50 

65  31 

+  0  02 

25  20 

25  10 

65  29 

.6768 

sw. 

68  18 

67  59 

-  0  48 

26  02 

25  52  ;   68  47 

.6601 

wsw. 

71  28 

71  09 

-  2  40 

26  42 

26  32  i   73  49 

.6424 

w. 

74  09 

74  43 

-  4  55 

27  56 

27  49 

7938 

.6202 

WNW. 

76  41 

77  15 

-  9  12 

28  34 

28  27 

86  27 

.6066 

NW. 

78  15 

78  49 

-13  02 

28  55 

28  48  I   91  51 

.5988 

NNW. 

78  49 

79  23 

-15  05 

2904 

28  57     94  28 

.5955 

Mean. 

72  20 

72  28 

-  6  31 

27  14 

27  14 

7859 

.6318 

In  the  case  of  this  dip  circle,  No.  35,  it  was  found  necessary  to  apply 
the  following  corrections  to  7  and  u  on  the  basis  of  the  results  of 

observations  at  several  shore  stations : 

/  '  u 

Circle  east,  needle  face  east — 23'  +  9' 

Circle  west,  needle  face  west +41  +  8 

Circle  west,  needle  face  east — 19  — 10 

Circle  east,  needle  face  west , +34  -  7 


102  OWRfjCJrfGSfcS   FOB   MAGNETIC    MEASUREMENTS. 


the  values  of  dip  and  total  intensity  show 
a  large  range  in  the  course  of  the  swing.  It  will  be  found  also  by  com- 
parison with  shore  observations  in  the  vicinity  that  the  mean  values 
of  dip  and  intensity  on  board  differ  by  considerable  amounts  from  the 
shore  results.  These  differences  do  not  remain  constant,  however, 
when  the  ship  goes  from  place  to  place.  The  deviations  in  dip  and 
total  intensity  may  be  derived  and  analyzed  in  a  manner  similar  to 
that  given  for  the  compass  deviations.  As  it  is  seldom,  however, 
that  dip-circle  observations  are  made  at  sea  except  when  swinging  ship , 
it  is  usually  sufficient  to  obtain  by  interpolation  from  the  swings  near 
shore  the  corrections  required  by  the  mean  values  of  dip  and  total 
intensity  for  the  swings  at  sea. 

For  the  limited  range  of  dip  usually  covered  in  a  season's  work  and 
with  swings  near  shore  in  the  highest  and  lowest  latitudes  reached,  a 
satisfactory  approximation  is  obtained  by  assuming  that  the  changes 
in  the  corrections  are  proportional  to  the  changes  in  dip. 

SPECIAL  DIRECTIONS. 

In  order  to  obtain  the  best  results  from  observations  on  shipboard 
especial  attention  should  be  paid  to  the  following  points: 

(1)  Avoid  as  far  as  possible  any  change  in  the  condition  of  the  intensity 
needles.     Keep  them  clean  and  free  from  rust  and  take  especial  care  to 
protect  the  pivots  from  injury.      When  removing  a  needle  after  observing 
be  sure  that  the  point  does  not  catch  on  the  edge  of  the  graduated  circle. 

(2)  Have  the  ship  as  nearly  as  possible  in  the  same  condition  as  regards 
location  of  boats,  anchors,  chains,  etc.,  for  the  swings  near  shore  as  for 
those  at  sea. 

(3)  Make  the  compass  observations  when  the  sun  is  not  more  than  30° 
high,  if  possible.     Steady  the  ship  on  a  heading  for  a  minute  or  two  before 
reading  the  sun's  bearing.     In  handling  the  azimuth  circle,  be  careful  to 
have  the  compass  bowl  swinging  free  at  the  moment  of  observation. 

(4)  When  there  is  much  motion  to  the  ship,  select  a  moment  for  talcing 
a  reading  when  she  is  nearly  on  an  even  keel.     In  the  case  of  the  dip 
circle,  select  a  vibration  of  the  needle  which  appears  symmetrical. 


DIRECTIONS  FOR  OPERATING  A  MAGNETIC  OBSERVATORY. 

BUILDINGS. 

For  the  operation  of  a  magnetic  observatory  there  are  required  a 
variation  building  in  which  the  variation  instruments  are  mounted, 
and  an  absolute  building  in  which  the  absolute  observations  are  made. 
In  their  construction  scrupulous  care  is  exercised  to  exclude  all 
material  that  might  possibly  affect  the  magnets,  and  in  their  subse- 
quent use  the  same  care  must  be  exercised.  No  article  of  magnetic 
material  should  be  carried  into  the  buildings  unless  absolutely 
needed,  and  no  person  should  be  allowed  to  enter  the  variation  build- 
ing until  he  has  divested  himself  of  all  such  articles,  as  knife,  watch, 
keys,  etc.  The  sole  of  a  shoe  or  the  brim  of  a  hat  often  contains  a 
piece  of  stsel  sufficient  to  disturb  the  sensitive  variation  instruments. 
Such  other  buildings  as  may  be  needed  are  usually  placed  far  enough 
away  to  have  no  effect  on  the  magnets.  The  variation  building  is 
designed  with  a  view  to  reduce  to  a  small  limit  the  range  of  temper- 
ature inside.  Those  of  the  Coast  and  Geodetic  Survey  are  all  above 
ground  and  built  of  wood,  the  amount  of  insulation  varying  with  the 
range  of  temperature  to  be  overcome. 

VARIATION  INSTRUMENTS. 

The  variations  in  declination,  horizontal  intensity,  and  vertical 
intensity  are  recorded  photographically  by  means  of  a  magneto- 
graph,  consisting  of  a  recording  apparatus  and  three  variometers. 
Light  from  a  lamp  is  reflected  from  a  mirror  attached  to  the  magnet 
of  a  variometer  and  traces  an  irregular  line  (curve)  on  a  sheet  of 
photographic  paper  (magnet ogram)  wrapped  around  a  revolving 
drum  of  the  recording  apparatus.  The  reflection  from  a  fixed 
mirror  traces  a  straight  line  (base  line)  on  the  magnetogram,  and  the 
variation  in  the  distance  between  the  curve  and  the  base  line  (ordi- 
nate)  is  a  measure  of  the  variation  in  the  direction  of  the  suspended 
magnet  produced  by  the  variation  in  the  earth's  magnetism. 

The  D  variometer  is  mounted  with  its  magnet  in  the  magnetic 
meridian  and  the  direction  of  the  magnet  changes  as  the  magnetic 
declination  changes.  In  the  H  variometer  the  magnet  is  suspended 
in  the  magnetic  prime  vertical  and  a  change  in  its  direction  corre- 
sponds to  a  change  in  the  horizontal  intensity.  In  the  Z  variometer 
the  magnet  rotatss  about  a  horizontal  axis,  like  a  dip  needle,  but  is 
adjusted  to  lie  approximately  in  the  horizontal  plane,  so  that  a 

103 


104  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

variation  in  its  inclination  to  the  horizon  corresponds  to  a  variation 
in  the  vertical  intensity. 

Each  of  the  five  observatories  of  the  Coast  and  Geodetic  Survey  is 
equipped  with  a  magnet  ograph  of  the  Eschenhagen  type,  in  which 
very  small  magnets  ar3  used,  so  that  it  is  possible  to  have  the  vari- 
ometers quite  near  to  each  other  without  appreciable  interaction. 
They  are  mounted  in  a  row,  magnetically  east  and  west,  as  shown  in 
Figure  10,  and  all  three  record  on  the  same  magnetogram,  the  up  and 
down  motion  of  the  Z  magnet  being  converted  to  horizontal  motion 
on  the  magnetogram  by  means  of  a  prism.  There  is  also  a  thermo- 
graph attached  to  the  vertical  intensity  variometer,  which  records 
photographically  the  variations  of  temperature. 

When  the  D  variometer  is  east  of  the  recording  apparatus,  a 
motion  of  the  north  end  of  the  magnet  to  the  east  (increasing  decli- 
nation) causes  the  registering  spot  of  light  to  move  to  the  north  on 
the  recording  drum.  When  it  is  west  of  the  recording  apparatus 
the  motion  of  the  spot  of  light  is  toward  the  south.  In  the  case  of 
the  horizontal  intensity  variometer,  when  the  north  end  of  the 


Magnetic  Prime  Vertical 


FIG.  10.— Relative  position  of  variometers. 


e 


magnet  points  toward  the  recording  apparatus,  an  increase  of  hori- 
zontal intensity  causes  the  spot  of  light  to  move  toward  the  north  on 
the  drum,  no  matter  whether  the  magnet  is  east  or  west  of  the 
recording  apparatus.  The  vertical  intensity  variometer  is  mounted 
with  the  north  end  of  the  magnet  to  the  north,  and  an  increase  of 
vertical  intensity  causes  the  spot  of  light  to  move  toward  the  south 
on  the  drum.  In  the  D  and  H  variometers  the  magnet  is  suspended 
by  means  of  a  quartz  fiber.  To  the  lower  end  of  the  fiber  is  attached 
a  light  frame  supporting  two  mirrors,  the  vertical  plane  surfaces  of 
which  make  a  slight  angle  with  each  other.  They  must  be  so 
adjusted  that  the  distance  between  the  two  reflected  rays  of  light, 
where  they  strike  the  recording  cylinder,  is  slightly  less  than  the 
width  of  the  magnetogram.  The  magnet  hangs  in  a  stirrup  attached 
to  the  lower  part  of  the  mirror  frame  and  is  inclosed  by  a  cylindrical 
copper  damping  box.  As  the  diameter  of  the  box  is  only  slightly 
greater  than  the  length  of  the  magnet  and  as  the  hole  in  the  top  is 
not  much  larger  than  the  shank  of  the  stirrup,  it  is  necessary  in 
adjusting  the  instrument  to  see  that  the  shank  is  centered  in  the  hole 
in  order  to  insure  freedom  of  motion  of  the  magnet,  and  the  observer 


VARIATION   INSTRUMENTS.  105 

should  examine  the  variometers- from  time  to  time  to  be  sure  that  no 
change  of  level  has  occurred.  The  moment  of  inertia  of  the  magnet 
system  is  so  small  that  only  a  very  small  resistance  is  required  to 
appreciably  affect  the  motion  of  the  magnet.  An  accumulation  of 
mold  or  dust,  or  the  web  of  a  minute  spider,  such  as  occasionally 
finds  its  way  through  the  openings  of  the  variometer,  is  often  suffi- 
cient. The  appearance  of  the  curve  will  usually  indicate  the  pres- 
ence of  an  obstruction,  and  it  may  be  necessary  to  remove  the  damp- 
ing boxes  and  clean  them  unless  it  is  found  that  change  of  level 
eliminates  the  trouble.  It  sometimes  happens  that  a  gradual  slip- 
ping of  the  joint  between  fiber  and  mirror  frame  causes  a  lowering  of 
the  magnet  in  its  damping  box  until  it  finally  touches  the  bottom. 

The  magnet  of  the  H  variometer  is  held  in  its  position  at  right 
angles  to  the  magnetic  meridian  principally  by  the  torsion  of  the 
supporting  fiber,  but  partly  also  by  control  magnets  placed  below 
the  suspended  magnet  with  their  axes  horizontal.  Their  primary 
object,  however,  is  to  regulate  the  sensitiveness  of  the  variometer. 

In  the  Z  variometer  there  are  two  magnets  supported  by  a  light 
frame,  like  the  beam  of  a  balance,  on  the  under  side  of  which  are 
two  conical  steel  points  which  rest  in  cup-shaped  depressions  in 
agate  surfaces.  The  steel  points  are  so  adjusted  that  the  line  joining 
them  is  at  right  angles  to  the  magnetic  axis  of  the  magnet  system. 
The  horizontality  of  the  magnet  is  secured  partly  by  an  adjustable 
weight  threaded  onto  a  horizontal  rod,  and  partly  by  a  control 
magnet  directly  under  the  center  of  the  magnet,  which  partly  coun- 
teracts the  effect  of  Z.  The  stability  is  regulated  by  a  weight 
threaded  onto  a  vertical  rod,  so  that  the  center  of  gravity  of  the 
magnet  system  may  be  raised  or  lowered,  as  desired.  Great  care 
must  be  exercised  in  working  about  this  variometer,  as  a  slight  jar  is 
sometimes  sufficient  to  change  the  balance  of  the  magnet  systsm  or 
even  throw  it  out  of  balance  altogether.  This  applies  especially  to 
the  deflection  observations  for  the  determination  of  scale  value. 
When  the  magnet  system  has  become  displaced  by  a  jar  or  by  an 
unusually  large  deflection,  as  during  a  magnetic  storm,  it  may  gen- 
erally be  put  back  in  adjustment  by  lifting  and  lowering  two  or 
three  times  by  means  of  the  lifter.  If  further  adjustment  is  required, 
it  can  usually  be  done  by  raising  or  lowering  the  control  magnet, 
unless  a  change  of  sensitiveness  is  required. 

Under  unfavorable  conditions  the  steel  bearing  points  may  become 
rusted  or  otherwise  blunted,  in  which  case  the  magnet  system  will  not 
move  freely  and  the  curve  will  appear  abnormally  smooth.  Extra 
bearing  points  are  provided  for  replacing  those  which  may  become 
defective. 

The  distance  between  the  D  and  Z  variometers  is  so  short  that  a 
change  in  the  position  of  the  Z  control  magnet  produces  a  slight 


106  DIRECTIONS   FOB   MAGNETIC    MEASUREMENTS. 

change  in  the  position  of  the  D  magnet,  and  the  amount  of  this  change 
must  be  determined  when  the  Z  variometer  is  readjusted. 

The  thermograph  consists  of  a  Bourdon  tube  filled  with  mercury, 
to  the  free  end  of  which  is  attached  a  mirror. 

The  drum  of  the  recording  apparatus  is  usually  made  to  revolve 
once  in  24  hours.  At  hourly  intervals  a  system  of  shutters  is  raised 
to  a  vertical  position  by  means  of  a  cam  attached  to  a  gear  wheel  and 
after  the  lapse  of  a  minute  or  two  allowed  to  drop  back  into  a  hori- 
zontal position.  The  shutters  are  so  adjusted  that  when  raised  they 
prevent  the  light  from  the  fixed  mirrors  reaching  the  magnetogram 
and  thus  produce  a  short  break  in  each  base  line. 

By  a  change  of  gearing  the  drum  may  be  made  to  revolve  once  in 
two  hours  and  the  time  breaks  then  occur  every  five  minutes.  It  is 
then  necessary  to  open  wider  the  slit  of  the  lamp,  in  order  to  secure 
sharp  lines  on  the  photographic  paper. 

CONVERSION  TO  ABSOLUTE  VALUES. 

In  order  to  determine  the  absolute  value  of  D,  H,  or  Z  at  any 
moment  from  the  continuous  photographic  record  of  the  variometer 
it  is  necessary  to  know:  (1)  The  base-line  value,  that  is,  the  absolute 
value  when  the  curve  and  base  line  coincide;  (2)  the  scale  value,  or 
value  of  1  millimeter  of  ordinate  expressed  in  absolute  units  (minutes 
for  D,  gammas  or  units  of  the  fifth  decimal  in  the  C.  G.  S.  system 
for  H  and  Z) ;  (3)  in  the  case  of  H  and  Z,  the  temperature  coefficient, 
or  the  effect  upon  the  ordinate  of  a  change  of  1°  in  temperature. 

In  the  H  variometer,  the  position  of  the  magnet  is  the  resultant 
effect  of  the  force  of  torsion,  the  force  acting  between  the  suspended 
magnet  and  the  control  magnets,  and  the  force  exerted  upon  the 
suspended  magnet  by  the  horizontal  component  of  the  earth's  field. 
A  change  in  the  magnetic  moment  of  the  suspended  magnet  due  to 
change  of  temperature  will  change  the  magnetic  force  acting  and  hence 
change  the  position  of  equilibrium,  irrespective  of  any  change  in  H. 

Similar  conditions  exist  in  the  Z  variometer  and  in  addition  the 
moment  of  the  balancing  weight  changes  with  temperature  on  account 
of  change  in  the  length  of  the  supporting  rod. 

Let  d,  7i,  2  =  the  ordinates  in  millimeters  at  the  temperature  t,  in- 
creasing ordinate  corresponding  to  increasing  D,  H,  and  Z, 

£d,  £h,  £z  =  scale  values  of  D,  H,  and  Z,  respectively, 

Bd,  Bh,  Bz  =  base-line  values  for  D,  H,  and  Z  (in  the  case  of  H  and 
Z,  reduced  to  a  standard  temperature  t0  , 

qh  and  qz  =  temperature  coefficients  of  the  H  and  Z  variometers, 

Then 

D  =  Bd+d.ed 

H  =  Bh+Ji.eh+qh(t-t0) 


CONVERSION   TO   ABSOLUTE   VALUES.  107 

BASE-LINE    VALUES. 

For  the  determination  of  the  base-line  values  absolute  observations 
are  made  at  least  once  a  week.  From  an  inspection  of  the  above  for- 
mulas it  will  be  seen  that  if  the  ordinates  d,  h,  z  be  read  for  the  times 
at  which  absolute  observations  have  been  made,  the  base-line  values 
may  be  computed,  provided  the  scale  values  and  temperature  coeffi- 
cients are  known.  The  absolute  value  of  vertical  intensity  must  be 
computed,  however,  from  the  observed  values  of  H  and  I.  It  is  in 
general  not  feasible  to  make  simultaneous  observations  of  H  and  1, 
but  the  value  of  H  at  the  time  of  the  dip  observations  may  be  deter- 
mined from  the  record  of  the  variometer  after  the  H  base-line  value 
has  been  computed. 

The  absolute  observations  are  made  in  the  manner  already  ex- 
plained, but  greater  care  must  be  exercised  in  the  operations  and  a 
greater  degree  of  accuracy  is  to  be  expected  than  is  the  case  in  work 
in  the  field.  Absolute  accuracy  is  impossible,  however,  and  the  base- 
line values  resulting  from  a  series  of  observations  will  show  more  or 
less  variation,  whereas  they  should  be  constant  provided  there  has 
been  no  change  in  the  adjustment  of  the  variometers.  It  has  been 
found  in  some  cases  that  even  when  there  has  been  no  readjustment 
of  the  variometer  the  base-line  values  show  a  progressive  change. 
This  may  be  due  partly  to  gradual  change  of  the  relative  positions  of 
suspension  fiber  and  stirrup,  partly  to  the  fact  that  the  magnets  suffer 
gradual  loss  of  magnetism  with  age  and,  in  the  case  of  H  and  Z  where 
the  range  of  temperature  has  been  large,  partly  to  error  in  the  adopted 
value  of  temperature  coefficient.  It  is  possible  also  that  the  torsion 
of  the  quartz  fibers  may  change  somewhat  with  age.  Hence  in  deter- 
mining what  base-line  values  to  adopt  it  is  necessary  to  adjust  the 
observed  values,  having  due  regard  to  this  progressive  change.  For 
any  particular  set  of  instruments  it  must  be  found  out  by  experience 
how  closely  the  adopted  values  should  correspond  to  those  resulting 
from  observation.  In  the  case  of  D  and  H  the  mean  of  the  values 
determined  in  the  course  of  a  month  is  usually  almost  free  of  error  of 
observation  and  may  be  used  as  a  basis  for  determining  the  gradual 
change  from  month  to  month.  In  the  case  of  Z  the  error  of  observa- 
tion is  somewhat  greater.  An  abrupt  and  continued  change  in  the 
base-line  values  when  there  has  been  no  readjustment  of  the  vario- 
meter would  demand  a  careful  examination  of  the  absolute  instru- 
ment to  make  sure  that  there  is  no  systematic  error  in  the  absolute 
observations  due  to  lack  of  adjustment.  It  is  desirable  to  make 
absolute  observations  at  different  times  of  the  day,  so  that  the  com- 
putation of  base-line  values  will  involve  ordinates  of  different  amounts. 
The  form  of  computation  of  H  and  Z  base-line  values  is  shown  in  the 
following  examples,  in  which  the  adopted  standard  temperature  is 
10°  C. 

m 


108 

Form  358. 


DIRECTIONS  FOB  MAGNETIC    MEASUREMENTS. 


HORIZONTAL  INTENSITY  BASE  LINE. 


Sitka,  Alaska.  Magnetic  Observatory. 
Magnetograph  No.  6. 


Magnetometer  No.  37. 


Date. 

Feb.  5.                   Feb.  11. 

Feb.  17. 

Feb.  20. 

1908.             L.  M.  T.     Scaling.     L.  M.  T. 

Scaling.     L.  M.  T. 

Scaling. 

L.  M.  T. 

Scaling. 

h.  m. 

mm.           h.  m. 

mm.           h.  m. 

mm. 

h.  m. 

mm. 

10  21             73.  4           14  40 

71.7            917 

73.6 

1005 

68.3 

Oscillations. 

24 
26 

79.4 
74.4 

43 
46 

69.3 
66.7 

20 
22 

73.7 
73.6 

08 
10 

68.1 
67.7 

29 

76.6 

48 

67.5               25 

73.4 

13 

67.4 

i 

10  41 

73.  8          15  00 

68.3           9  36 

72.0 

10  28 

66.5 

Deflections. 

47 
52 

74.4 
74.4 

06 
11 

68.9               41 
69.3                46 

71.4 
71.4 

33 
39 

67.6 
66.0 

58 

72.7 

17 

69.6 

51 

71.3 

44 

65.4 

I 

11  07 

72.9 

15  21 

70.3 

956 

71.2 

1048 

65.3 

Deflections. 

71.8 
71.6 

26 
32 

70.  1           10  01 
70.1                06 

70.1 
69.8 

53 

58 

64.9 
64.6 

22 

69.4 

37 

69.1 

11 

69.4 

11  04 

•  ;-}.  :, 

11  29 

65.3 

15  45 

69.5 

10  19 

68.3 

11  12 

63.5 

Oscillations. 

32 
34 

63.3 
61.3 

4X 
50 

69.3 
70.0 

21 
24 

68.5 
68.7 

15 
18 

63.5 
63.4 

37 

59.3 

53 

69.5 

27 

68.6 

20 

63.4 

Mean 

70.9 

69.3 

70.9 

65.6 

r 

r 

r 

r 

c* 

2.79 

2.79 

2.79 

2.79 

*  and  At 

3°.  7 

196 

5°.  9 

193 

5°.  7 

198 

6°.  5 

183 

4 

-46 

-30 

-31 

-26 

ft, 

152 

163 

167 

157 

H 

15536 

15552 

15555 

15537 

Base  line 

15384 

15389 

15388 

15380 

CONVERSION   TO   ABSOLUTE   VALUES. 


109 


Form  359. 


Sitka  Magnetic  Observatory. 
Magnetograph  No.  6. 


VERTICAL  INTENSITY  BASE  LINE. 

Earth  inductor  No.  2. 


Date. 

Feb.  5. 

Feb.  11. 

1908. 

Local 
mean  time. 

Scalings. 

Local 
mean  time. 

Scalings. 

H. 

Z. 

H. 

Z. 

h.     m. 

mm. 

mm. 

h.     m. 

mm. 

mm. 

9  29 

77.2 

-88.1 

16  25 

71.3 

-80.6 

31 

77.6 

88.1 

27 

70.7 

80.9 

34 

77.4 

87.7 

30 

72.1 

81.2 

36 

77.4 

87.5 

32 

71.3 

81.3 

39 

79.4 

87.4 

34 

72.8 

80.7 

41 

79.4 

87.3 

36 

73.3 

80.5 

44 

78.2 

86.7 

39 

73.3 

80.6 

Means 

(i-T.ar) 

78.1 

-87.5 

72.1 

-80.8 

Sh  and  £Z 

2.79 

4.69 

2.79 

4.69 

t  and  ht 

3.8 

r 
218 

5.9 

r 
201 

At  and  Ah 

6.2 

-45 

4.1 

-30 

h 

173 

171 

H  base  line 

at  10° 

15386 

15386 

H 

15559 

15557 

I 

74°  36'.  4 

74°  37'.  0 

logH 
log  tan  7 

4.  19198 
0.  56016 

4.  19193 
0.  56046 

logZ 

4.  75214 

4.  75239 

Z 

(J—  l.Or)                          r 
56512 

o 

r 
56544 

t  and  2< 

3.8                       -410 

5.9 

-379 

J£  and  Az 

6.2                          +6 

4.1 

+  4 

2 

-404 

-375 

Z  base  line 

at  10°                      56916 

56919 

SCALE    VALUES. 

From  the  formulas  on  page  106  it  would  appear  that  the  scale 
value  of  a  variometer  might  be  determined  by  making  absolute 
observations  at  different  times  and  comparing  the  change  in  the 
observed  values  with  the  change  in  ordinate.  In  practice,  however, 
the  uncertainty  in  the  absolute  observations  is  generally  too  great 
to  secure  satisfactory  results  in  this  way. 

The  scale  value  of  the  D  variometer  depends  directly  upon  the  dis- 
tance between  the  movable  mirror  of  the  magnet  and  the  paper  on 
the  drum,  and  is  found  by  the  formula — 


ctnl 


110  DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 

in  which  £d  is  the  angular  motion  of  the  magnet  corresponding  to  1  mm 
on  the  magnetogram,  R  is  the  distance  from  the  magnetogram  to 
the  face  of  the  movable  mirror  increased  by  two-thirds  the  thickness 
of  the  mirror,  and  li  is  the  angle  through  which  the  magnet  is  turned 
when  the  torsion  head  is  turned  through  the  angle/.  The  lens  of 
the  Eschenhagen  D  variometer  is  usually  focussed  for  a  scale  value 
of  1  mm.  =  1'.  For  this  convenient  scale  value — 

mm 

#=1718.c 


There  is  so  little  variation  in  the  torsion  of  a  quartz  fiber  that  after 
its  torsion  factor  has  once  been  determined  it  is  unnecessary  to 
repeat  the  operation,  although  it  is  usual  to  do  so  from  time  to  time 
as  a  check.  When  a  new  fiber  is  inserted,  a  determination  of  its 
torsion  factor  is  of  course  required. 

In  the  case  of  the  H  variometer,  the  scale  value  depends  upon  the 
rigidity  with  which  the  magnet  is  held  in  its  position  at  right  angles 
to  the  magnetic  meridian.  In  the  older  form  of  suspension  (bi-lilar) 
the  desired  sensitiveness  is  secured  by  varying  the  distance  between 
the  upper  ends  of  the  two  supporting  fibers.  Where  quartz  fiber 
suspension  is  used,  it  is  not  practicable  to  regulate  the  sensitiveness 
by  the  size  of  the  fiber,  but  the  desired  result  is  obtained  by  means 
of  control  magnets,  which  serve  to  increase  or  decrease  the  force  to 
be  balanced  by  the  torsion  of  the  fiber. 

The  scale  value  is  found  by  comparing  the  amounts  by  which  an 
auxiliary  magnet  deflects  the  magnets  of  the  D  and  H  variometers,; 
when  similarly  placed  with  regard  to  them.  The  series  of  observa- 
tions is  begun  by  deflecting  the  D  magnet  by  placing  the  deflector  to 
the  east  and  west  (in  the  magnetic  prime  vertical),  north  end  east  or 
west.  Then  the  H  magnet  is  deflected  by  placing  the  deflector  to  the 
north  and  south,  north  end  north  or  south.  This  is  followed  by  a 
second  set  of  D  deflections.  Unless  the  torsion  of  the  D  fiber  is 
known  from  previous  observations,  a  set  of  observations  to  deter- 
mine that  factor  is  also  require^.  It  is  important  to  make  deflec- 
tions at  two  distances  as  a  check  on  the  accuracy  of  the  work. 
Such  distances  should  be  selected  as  will  give  deflections  of  consider- 
able magnitude  without  throwing  the  spot  of  light  beyond  the  limits 
of  the  magnetogram.  Care  must  be  taken  to  use  the  same  deflection 
distances  on  both  variometers  and  to  have  the  deflector  in  the  same 
horizontal  plane  with  the  deflected  magnet. 

It  is  evident  that  the  effect  of  the  deflector  on  the  //  magnet 
corresponds  to  an  increase  or  decrease  of  the  horizontal  intensity  by 
an  amount  equal  to  the  intensity  of  the  field  of  the  deflector  at  the 
selected  distance.  The  amount  by  which  the  D  magnet  is  deflected 
depends  upon  the  relative  intensity  of  the  earth's  field  and  that  of 
the  deflector  at  the  selected  distance. 


CONVERSION   TO   ABSOLUTE   VALUES.  Ill 

Let  ^  =  the  number  of  millimeters  which  the  D  spot  is  deflected. 
£7=  the  angle  through  which  the  D  magnet  is  deflected. 
uf  =  the  number  of  millimeters  which  the  H  spot  is  deflected. 
£h  =  H  scale  value,  i.  e.,  the  change  in  H,  expressed  in  gammas, 

corresponding  to  a  change  in  ordinate  of  1  mm. 
W=  field  intensity  of  the  deflector  at  the  selected  distance. 
In  the  case  of  the  H  deflections : 

eh.u'=W 
In  the  case  of  the  D  deflections : 

,  =  flu  tan  IV   /   \Bu( 


Since  the  deflection  angle  is  always  small  its  tangent  may  be  taken 
as  proportional  to  the  angle  and  we  have  just  seen  that  the  D  scale 
value  is 


Hence 

,     Hu/    f   \  2u      H  /    f 


As  the  deflection  observations  give  directly  the  values  of  2u  and  2u', 
it  is  more  convenient  to  introduce  a  2  in  both  numerator  and  denomi- 
nator of  the  formula  and  use  it  in  the  form  given.  It  has  already 
been  pointed  out  that  there  is  very  little  variation  in  the  torsion 
coefficient  of  a  quartz  fiber.  The  distance  between  the  D  mirror  and 
the  drum  is  constant  so  long  as  there  is  no  readjustment  and  H  may 
be  assumed  as  constant  for  a  year  without  introducing  a  material 
error  in  the  scale  value  computation.  Hence,  for  that  period  the 

H        / 
factor  H^>  '  yriTT  maJ  be  regarded  as  constant  and  the  formula  be- 

comes simply 

£fc  =  ^(constant 

The  form  of  observation  and  computation  is  shown  in  the  following 
example.  It  will  be  noticed  that  the  two  results  from  deflections 
at  different  distances  do  not  agree  exactly.  A  comparison  of  the  H 
ordinates  for  times  when  the  deflector  was  not  in  use  with  the  deflected 
ordinates  shows  that  the  deflections  were  unsymmetrical,  the  amount 
of  deflection  being  greater  when  the  ordinate  was  decreased  than 
when  it  was  increased.  It  has  been  found  that  under  certain  condi- 
tions of  adjustment,  as  in  this  case,  the  scale  value  varies  with 
the  position  of  the  magnet  and  may  be  represented  analytically  as 
a  linear  function  of  the  ordinate. 


112 


DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 


A  comparison  of  the  different  determinations  at  Cheltenham  in  1909 
gives  the  value  J5  =  .004.  The  mean  of  the  scalings  for  the  short 
deflection  distance  is  13.0  mm.  and  for  the  long  distance  18.3  mm., 
and  the  resulting  scale  values  should  differ  by  about  0.02^,  as  they 
do.  When  adjusting  the  variometer,  the  control  magnets  should  be 
so  placed  that  the  deflections  are  symmetrical  or  nearly  so. 

It  sometimes  happens  during  deflections  that  the  regular  spot  of 
light  is  thrown  off  the  magnetogram  and  a  record  is  made  by  the 
reserve  spot.  In  such  cases  the  two  spots  must  be  made  to  record  at 
the  same  time  at  the  close  of  the  observations,  so  that  the  distance 
between  them  may  be  measured. 

Form  373. 


H  SCALE  VALUE. 

ate,  May  26,  1909.                                     Magnetograph  No.  5. 

Observer,  J.  E.  Durban 

.J 

I. 

II. 

o 

Distance—  26  cm. 

Distance—  31  cm. 

a 

Remarks. 

I 

a 

J 

No. 

Scaling. 

Diff. 

No. 

Scaling. 

Diff. 

i 

mm. 

mm. 

mm. 

mm. 

D 

E 

E 

1 

38.0 

4 

46.1 

E 

W 

2 

78.0            «° 

3 

70.0 

23.9 

W 

W 

8 

77.9 

I 

69.8 

W 

E 

7 

38.1 

39.8 

46.4 

B.« 

H 

N 
N 

N 
S 

1 
2 

91.1 
-66.9 

158.0 

4 
3 

64.6 
-28.8 

93.4 

S 
S 

S 

N 

8 
7 

-65.6 
93.2 

158.8 

5 
6 

-27.9 
65.2 

93.1 

D 

W 

E 

1 

37.9 

4 

46.0 

39.9 

21 

.7 

W 

W 

2 

77.8 

3 

69.7 

' 

E 
E 

W 

E 

8 
7 

78.0 
37.8 

40.2 

6 

69.9 

45.8 

24.1 

* 

D 

2  u            39.  98 

2tt 

23.78 

H 

2  u'         158.  40 

2tt' 

93.25 

Scalings  with  magnet  away. 

Torsion  observations. 

L.M.T. 

Scaling. 

Temp.                  Remarks. 

"ch-cle"     ScalinS-        Diff- 

h.  m. 

mm. 

, 

mm.           mm. 

D 

11  02 

57.7 

Beginning  of  first  set. 

133             57.4 

D 

11  19 

58.1 

End  of  first  set. 

163             »-8            56.0 

H 

11  19 

21.0 

24.  6    :  Beginning  of  set. 

103             85.3 

H 

11  33 

21.6 

24.7       End  of  set. 

133             57.  1 

D 

11  48 

57.8 

End  of  second  set. 

Sum           112.3 

Mean  for  30°            28.  1 

CONVERSION   TO   ABSOLUTE   VALUES. 


113 


COMPUTATION. 
.K=  1720.1  mm.          H=19880r 


I. 

1 
1 

II. 

Iog2w 

1.6018 

1.  3762 

"   H 

4.  2984 

/    f    \ 

0.0068 

t(   (j^h) 

0.  7686 

colog  2R                      6.  4634 

"    2u' 

7.8002 

8.  0304 

log,                             0.1706 

0.  1752 

c                               I-  481 

1.497 

Mean                         1.  49 

The  scale  value  of  the  vertical  intensity  variometer  is  determined 
in  a  similar  manner,  but  the  deflector  is  placed  differently.  When 
deflecting  the  D  magnet  the  deflector  is  placed  to  the  north  or  south 
(magnetic)  of  the  D  variometer,  with  its  axis  directed  magnetically 
east  and  west.  When  deflecting  the  Z  magnet  it  is  placed  to  the 
north  or  south,  with  its  axis  vertical.  The  formula  for  computing 
the  Z  scale  value  is  of  the  same  form  as  that  derived  for  J?,  namely: 


f 


_2u 
£z~2u'  2 

u'  in  this  case  being  the  number  of  millimeters  which  the  Z  spot  is 
deflected. 

Great  care  must  be  exercised  when  placing  the  deflector  in  the 
various  positions  in  order  not  to  jar  the  variometer,  and  thus  alter 
the  adjustment.  The  ordinate  with  deflector  away  should  be  read 
at  the  beginning  and  end  of  the  set,  to  show  whether  or  not  a  change 
has  taken  place  during  the  observations. 

At  Cheltenham,  where  two  magnetographs  are  in  operation,  the 
scale  value  of  the  Adie  Z  variometer  is  determined  by  the  method 
explained  above,  but  that  of  the  Eschenhagen  variometer  is  obtained 
by  comparing  the  daily  range  as  given  by  the  two  variometers. 

TEMPERATURE    COEFFICIENTS. 

When  the  variation  building  is  well  insulated,  so  that  the  diurnal 
variation  of  temperature  inside  is  limited  to  a  few  tenths  of  a  degree 
Centigrade  and  the  seasonal  variation  is  very  gradual,  only  approxi- 
mate values  of  the  temperature  coefficients  of  the  H  and  Z  vari- 
ometers are  required.  They  may  sometimes  be  determined  from  the 
regular  observatory  records  by  selecting  periods  free  from  large  dis- 
turbances during  which  there  was  both  a  rise  and  fall  of  temperature. 
A  comparison  of  the  mean  of  the  24  hourly  ordinates  for  the  days  of 
77213—11 8 


114 


DIRECTIONS  FOR  MAGNETIC    MEASUREMENTS. 


high  temperature  with  the  corresponding  mean  for  the  days  of  low 
temperature  shows  the  effect  of  change  of  temperature.  The  follow- 
ing example  will  illustrate  the  method : 


Date. 

Temper- 
ature. 

Mean  ordinate. 

1907. 
Jan.  21,  22,  29,  30 

0 

-6.79 

mm. 
93.55 

Jan.  23,  24,  25,  26 
Differences 

-2.96 

95.15 

3.83 

1.60 

1.60 

'-sTS*4-41-1'* 

being  the  scale  value;  that  is,  an  increase  of  1°  in  temperature 
corresponds  to  an  increase  in  the  ordinate  of  1.9f.  In  using  this 
method  great  care  must  be  exercised  in  the  selection  of  the  periods  in 
order  to  eliminate  as  far  as  possible  changes  in  ordinate  due  to  other 
causes  than  change  in  temperature,  and  an  adopted  value  of  temper- 
ature coefficient  should  depend  on  a  number  of  such  determinations. 
Where  the  insulation  is  so  good  that  the  temperature  in  the  variation 
building  does  not  change  sufficiently  to  use  .the  above  method,  the 
instrument  room  may  be  heated  and  cooled  artificially.  For  success- 
ful results  the  changes  of  temperature  should  be  so  gradual  that  the 
temperature  of  the  magnet  will  be  correctly  represented  by  the  ther- 
mometer readings  and  a  time  should  be  selected  when  the  changes  in 
H  and  Z  are  apt  to  be  small,  unless  a  second  magnetograph  is  in  oper- 
ation and  may  be  used  to  determine  those  changes. 

In  the  case  of  the  H  variometer  there  is  no  reason  to  expect  a 
change  of  temperature  coefficient.  With  the  Z  variometer,  how- 
ever, the  factors  making  up  the  temperature  coefficint  are  so  hetero- 
geneous that  a  radical  change  of  adjustment  may  produce  a  change  of 
temperature  coefficient. 

TEMPERATURE. 

In  order  to  determine  the  temperature  of  the  magnets  from  the 
record  of  the  thermograph,  the  thermometers  attached  to  the  H  and 
Z  variometers  are  read  morning  and  afternoon  at  times  which  corre- 
spond approximately  with  the  daily  extremes  of  temperature. 
Under  ordinary  conditions  the  variations  in  temperature  may  be 
assumed  to  be  the  same  for  the  two  variometers.  The  change  in 
thermometer  reading  between  morning  and  afternoon  compared  with 
the  change  in  ordinate  of  the  thermograph  curve  will  serve  to  deter- 
mine the  scale  value  of  the  thermograph. 


PROGRAMME   OF   WORK.  115 

TIME  SCALE. 

The  recording  apparatus  is  provided  with  suitable  mechanism  for 
making  a  short  break  in  the  base  lines  at  intervals  of  an  hour.  The 
exact  time  of  occurrence  of  the  first  and  last  time  breaks  on  each 
magnetogram,  as  well  as  of  one  occurring  in  the  morning,  is  deter- 
mined by  the  click  made  by  the  mechanism  when  the  shutters  are 
raised  and  lowered.  The  times  of  stopping  and  starting  the  drum  are 
also  recorded. 

Time  observations  are  made  often  enough  to  insure  a  knowledge  of 
the  chronometer  correction  on  local  mean  time  to  the  nearest  tenth  of 
a  minute. 

READING  OF  ORDINATES. 

It  is  customary  to  tabulate  the  hourly  ordinates  of  D,  H,  and  Z 
and  also  the  maximum  and  minimum  values  for  each  day  and  from 
them  to  compute  the  corresponding  absolute  values.  Local  mean 
time  is  used  and  the  hours  are  counted  from  midnight  to  midnight, 
0  to  24.  For  the  determination  of  the  base-line  values,  ordinates 
must  be  measured  for  the  times  when  absolute  observations  were 
made.  In  the  case  of  the  vertical  intensity,  H  as  well  as  Z  ordinates 
must  be  measured  for  the  time  covered  by  the  dip  observations, 
in  order  that  the  value  of  H  may  be  obtained  for  combining  with  7  to 
compute  Z.  The  number  of  ordinates  to  be  read  for  a  base-line 
determination  depends  upon  the  irregularity  of  the  curve  at  that 
time.  At  the  Coast  and  Geodetic  Survey  observatories  the  ordinates 
are  measured  from  the  bottom  of  the  base  line  to  the  bottom  of  the 
curve  and  at  right  angles  to  the  base  line.  It  is  generally  found  that 
the  perpendicular  at  the  end  of  the  base  line  does  not  pass  through 
the  end  of  the  curve,  and  this  fact  must  be  allowed  for  when  deter- 
mining the  time  scale.  For  measuring  the  ordinates  a  reading  board 
has  been  found  very  useful.  A  picture  and  description  of  it  will  be 
found  in  "  Results  of  Observations  at  the  Coast  and  Geodetic  Survey 
Magnetic  Observatory  at  Cheltenham,  Md.,  1901-1904." 

PROGRAMME  OF  WORK. 

While  the  routine  of  an  observatory  is  affected  somewhat  by  local 
conditions,  the  following  programme  of  work  to  be  done  will  be  modi- 
fied only  in  minor  details : 

(1)  Enter  the  variation  room  in  the  morning  in  time  to  record  the 
8  o'clock  time  break.     Read  the  thermometers,   wind  the  driving 
clock,  see  that  the  lamp  is  burning  brightly  and  that  the  spots  of 
light  are  recording  properly.     Make  psychrometric  observations. 

(2)  Compare  the  timepiece  used  with  the  standard  chronometer 
and  wind  both  of  them. 


116  DIRECTIONS  FOR   MAGNETIC    MEASUREMENTS. 

(3)  Put  new  sheets  of  paper  on  the  seismograph,  recording  the 
times  of  stopping  and  starting  the  drums.     Wind  the  clocks  when 
necessary. 

(4)  Make  meteorological  observations  in  the  open  air. 

(5)  Enter  the  variation  room  in  the  afternoon  in  time  to  record 
the  time  break  at  16  hours.     Read  the  thermometers.     Remove  the 
magnetogram,  prick  holes  for  measuring  shrinkage,  date  and  put  on 
a  new  sheet  of  paper,  wind  the  clock,  trim  the  lamp  wick  and  adjust 
the  light.     The  lamp  requires  filling  every  other  day.     Record  the 
times  of  stopping  and  starting  the  drum. 

(6)  Record  the  time  break  at  17  hours.     Read  the  thermometers. 
Examine  the  lamp  and  spots  of  light. 

The  clock  will  run  for  more  than  24  hours,  but  a  more  uniform  rate 
can  usually  be  secured  by  winding  twice  a  day.  When  doing  any 
work  in  the  instrument  room  requiring  light,  a  ruby  lamp  should  be 
used  or  else  the  front  of  the  recording  box  should  be  closed. 

Absolute  observations  are  made  at  least  once  a  week,  always  on 
the  same  day  of  the  week.  A  week's  observations  comprise  two  or 
three  sets  of  declination,  two  sets  of  horizontal  intensity,  and  two  or 
three  sets  of  dip.  About  once  a  week  the  magnetograms  are  devel- 
oped and  the  seismograms  are  fixed. 

With  a  good  chronometer  time  observations  four  or  five  times  a 
month  will  suffice. 

Deflections  for  the  determination  of  H  and  Z  scale  values  are  made 
at  least  once  a  month.  In  case  of  a  readjustment  the  scale  value 
should  be  determined  just  before  the  adjustment  and  again  two  or 
three  days  afterwards. 

GENERAL  DIRECTIONS. 

Magnetograph  record. — The  magnetograph  record  should  contain  a 
detailed  account  of  whatever  happens  to  any  one  of  the  component 
parts  of  the  magnetograph,  so  that  the  computer  will  have  collected 
in  one  place  all  the  information  needed  to  properly  interpret  the 
results.  If  the  H  variometer  is  adjusted  by  turning  the  torsion  head, 
the  amount  and  direction  of  change  should  be  recorded.  If  the  posi- 
tion of  the  control  magnets  is  changed,  their  position  with  respect  to 
the  suspended  magnet  and  each  other,  both  before  and  after  the 
change,  should  be  recorded.  Similar  record  should  be  made  of  any 
change  in  the  weights  or  control  magnet  of  the  Z  variometer.  Any 
change  of  adjustment  which  produces  a  change  of  base-line  value 
should  be  noted  also  on  the  base-line  computation  and  on  the  monthly 
tabulation  of  hourly  values. 

Adjustments. — It  is  important  to  make  a  direct  determination  of 
the  effect  of  an  adjustment,  if  possible.  For  that  reason  it  is  desir- 
able to  have  a  magnetogram  on  the  drum  at  the  time,  so  that  a  com- 


GENEKAL  DIRECTIONS.  117 

parison  may  be  made  of  the  relative  position  of  the  spots  of  light 
before  and  after  the  adjustment.  Deflections  for  the  determination 
of  scale  value  should  be  made  just  before  a  readjustment  and  again 
two  or  three  days  later.  When  readjusting  the  H  variometer,  the 
effort  should  be  made  to  place  the  control  magnets  in  such  a  position 
as  to  give  a  constant  scale  value.  If  the  deflections  are  symmetrical 
about  the  undeflected  position  of  the  magnet,  it  is  safe  to  assume 
that  the  desired  result  has  been  obtained.  The  amount  of  deflection 
on  H  or  Z  corresponding  to  a  desired  scale  value  can  be  readily  com- 
puted from  the  formula  when  the  amount  of  deflection  of  D  at  the 
same  distance  is  known.  (Compare  formula  on  page  111.) 

Arrangement  of  spots. — The  spots  of  light  should  be  so  arranged  as 
to  secure  as  complete  and  distinct  a  record  as  possible.  The  relative 
position  of  curve  and  base  line  should  be  such  that  increasing  ordi- 
nates  correspond  to  increasing  values  of  the  element.  Small  ordinates 
are  preferable,  but  a  mixture  of  positive  and  negative  ordinates  is 
apt  to  give  rise  to  mistakes.  It  is  undesirable  to  have  the  curves 
so  near  to  each  other  that  there  will  be  many  crossings.  As  the  usual 
effect  of  a  magnetic  storm  is  to  diminish  the  horizontal  intensity,  the 
H  variometer  should  be  so  adjusted  that  the  reserve  spot  will  come 
on  at  the  top  of  the  magnetogram  when  the  regular  spot  goes  off  at 
the  bottom.  To  avoid  confusion  the  D  variometer  should  be  adjusted 
so  that  the  reserve  spot  will  come  on  at  the  bottom. 

Amount  of  light. — It  should  be  borne  in  mind  that  during  a  mag- 
netic disturbance  the  motion  of  the  magnet  is  much  more  rapid  than 
on  a  quiet  day,  and  consequently  a  greater  volume  of  light  is  required 
to  record  its  motion  on  the  photographic  paper. 

Reading  of  ordinates. — All  ordinates  are  to  be  read  and  checked  at 
the  observatory.  When  making  the  second  reading  special  atten- 
tion should  be  directed  to  the  elimination  of  gross  errors,  as,  for 
example,  misreadings  of  5  or  10  mm.,  reading  from  the  wrong  base 
line,  or  reading  base-line  ordinates  on  the  wrong  day.  Base-line  ordi- 
nates should  be  read  at  the  same  time  as  the  hourly  values.  The 
maximum  and  minimum  ordinates  should  be  compared  with  the 
hourly  values  on  the  same  day  as  a  check  against  misreadings. 

Correction  for  shrinkage  will  be  made  when  necessary.  Declina- 
tion scalings  will  be  converted  at  once  to  minutes  (except  in  scale- 
value  deflections,  where  they  are  to  be  recorded  in  millimeters)  with 
the  aid  of  a  suitable  table,  giving  the  limiting  ordinates  between  which 
a  certain  correction  is  required  to  convert  millimeters  to  minutes. 
The  torsion  factor  must  always  be  included  in  computing  the  D  scale 
value. 

Magnetograph  temperatures  will  be  obtained  directly  from  the 
photographic  record  of  the  Z  thermograph,  if  possible,  based  on  the 
mean  of  the  H  and  Z  thermometer  readings  (corrected).  If  the  varia- 


118  DIRECTIONS  FOR  MAGNETIC   MEASUREMENTS. 

tion  in  temperature  is  so  small  that  the  thermograph  trace  appears 
as  a  straight  line  between  two  consecutive  thermometer  readings,  the 
magnetograph  temperatures  may  be  obtained  by  interpolation  between 
the  thermometer  readings. 

The  daily  means  will  be  computed  on  all  the  monthly  tabulation 
sheets,  but  the  hourly  means  are  required  for  declination  only.  A 
day  from  which  some  hourly  values  are  missing  or  on  which  a  change 
of  base-line  value  occurred  will  be  omitted  in  taking  means.  Missing 
hourly  values  may  be  supplied  by  interpolation  when  they  are  only 
few  in  number  and  occur  in  a  period  comparatively  free  from  disturb- 
ance. 

Magnetic  character  of  day. — The  magnetic  character  of  the  two 
halves  of  each  day,  a.  in.  and  p.  m.,  will  be  indicated  roughly  by  the 
figures  0,  1,  2  on  the  monthly  tabulation  for  each  element,  and  the 
character  of  each  Greenwich  day  as  a  whole  will  be  tabulated  on  the 
same  scale,  and  this  tabulation  (in  duplicate)  will  be  forwarded  to 
the  Office  as  soon  as  possible  after  the  end  of  the  quarter.  At  the 
same  time  there  will  be  transmitted  a  table  giving  the  times  of  occur- 
rence and  duration  of  the  principal  magnetic  disturbances  occurring 
during  the  quarter. 

Absolute  observations  will  be  made  at  least  once  a  week.  When 
field  instruments  are  to  be  compared  with  the  observatory  instru- 
ments for  purposes  of  standardization  and  two  observers  are  available, 
it  is  preferable  to  make  simultaneous  observations,  exchanging  the 
positions  of  the  instruments  in  the  middle  of  the  series  in  case  the 
relation  of  the  two  stations  is  not  known.  Where  this  plan  can.  not 
be  carried  out,  base-line  ordinates  will  be  read  for  the  observations 
with  the  field  instruments,  so  that  allowance  may  be  made  for  the 
variation  of  the  earth's  magnetism  between  the  observations  with  the 
two  sets  of  instruments. 

Transmission  of  records. — The  observatory  records  will  be  forwarded 
to  the  office  monthly,  as  soon  as  the  necessary  computations  have 
been  completed.  To  guard  against  loss  of  records  in  transmission,  a 
summary  of  the  results  of  absolute  observations  and  a  copy  of  the 
monthly  tabulations  of  variation  observations,  base-line  determina- 
tions, etc.,  must  be  retained  at  the  observatory.  Such  a  summary 
is  needed  by  the  observer  in  order  that  he  may  exercise  proper  control 
over  the  observatory  work. 


TABLES. 

TABLE  I. 
Correction  to  observed  altitude  of  the  sun  for  refraction  and  parallax. 


119 


Apparent 
altitude. 

Temperature,  centigrade. 

Apparent 
altitude. 

-10° 

0°     +10° 

+20° 

+30° 

+40° 

5 

10  33 

10  07     9  43 

9  21 

9  00 

8  40 

5 

6 

9  01 

8  39    8  19 

8  00 

7  42 

7  25 

6 

7 

7  51 

7  32 

7  15     6  59 

6  44 

6  30 

7 

8 

6  55 

6  39 

6  24 

6  10 

5  57 

5  44 

8 

9 

6  12 

5  58 

5  44 

5  32 

5  20 

5  08 

9 

10 

5  35 

5  22 

5  10     4  59 

4  48 

4  38 

10 

11 

5  05 

4  53 

4  42     4  32 

4  22 

4  13 

11 

12 

4  40 

4  29 

4  19     4  10 

4  01 

3  52 

12 

13 

4  17 

4  07 

3  58    3  50 

3  42 

3  34 

13 

14 

3  59 

3  50 

3  41     3  33 

3  25 

3  18 

14 

15 

3  41 

3  33 

3  25     3  18 

3  11 

3  05 

15 

16 

3  28 

3  21 

3  13     3  06 

3  00 

2  54 

16 

17 

3  14 

3  07 

3  00     2  54 

2  48 

2  43 

17 

18 

3  04 

2  57 

2  50     2  44 

2  38 

2  33 

18 

19 

2  53 

2  47 

2  40 

2  34 

2  29 

2  24 

19 

20 

2  43 

2  37 

2  31     2  26 

2  21 

2  16 

20 

21 

2  34 

2  28 

2  23     2  18 

2  13 

2  09 

21 

22 

2  25 

2  20 

2  15     2  10 

2  06 

2  02 

22 

23 

2  18 

2  13  * 

2  08     2  04 

1  59 

1  55 

23 

24 

2  12 

2  06 

2  02     1  58 

1  54 

1  50 

24 

25 

2  05 

2  00 

1  56     1  52 

1  48 

1  45 

25 

26 

2  00 

1  55 

1  51     1  47 

1  43 

1  40 

26 

27 

1  55 

1  50 

1  46     1  42 

1  38 

1  35 

27 

28 

1  49 

1  44 

1  41     1  38 

1  34 

1  30 

28 

29 

1  45 

1  40 

1  37     1  34 

1  30 

1  26 

29 

30 

1  41 

1  36 

1  33     1  30 

•1  27 

1  23 

30 

32 

1  32 

1  28 

1  25     1  22 

1  19 

1  16 

32 

34 

1  25 

1  21 

1  18     1  15 

1  13 

1  10 

34 

36 

1  19 

1  15 

1  13     1  10 

1  08 

1  05 

36 

38 

1  13 

1  09 

1  07     1  05 

1  03 

1  00 

38 

40 

1  07 

1  04 

1  02 

1  00 

0  58 

056 

40 

42 

1  03 

1  00 

0  58 

0  56 

0  54 

0  53 

42 

44 

0  58 

0  55 

0  53 

0  51 

0  49 

0  48 

44 

46 

0  54 

0  52 

0  50 

0  48 

0  46 

0  45 

46 

48 

0  51 

0  49 

0  47 

0  45 

0  43 

0  42 

48 

50 

0  47 

0  45 

0  43 

0  41 

0  40 

0  39 

50 

55 

0  38 

0  36 

0  35 

0  34 

0  32 

0  30 

55 

60 

0  31 

0  30 

0  29 

0  28 

0  27 

0  25 

60 

65 

0  25 

0  24- 

0  23 

0  22 

0  21 

0  20 

65 

70 

0  19  j   0  19 

0  18 

0  17 

0  17 

0  16 

70 

75 

0  14 

0  14 

0  13 

0  12 

0  12 

0  11 

75 

80 

0  09 

008 

0  08 

0  08 

0  07 

0  07 

80 

85 

0  04    0  04 

0  04  !   0  04 

0  03 

0  03 

85 

9fl 

0  00 

0  00 

0  00    0  00 

0  00 

0  00 

90 

120  DIRECTIONS  FOR  MAGNETIC    MEASUREMENTS. 

TABLE  II. 
Correction  in  azimuth  and  altitude  of  the  sun  for  semidiameter. 

Altitude  correction=  Semidiameter. 
Azimuth  correction— Semidiameter-f- cos  ft. 


Date. 

Altitude 
correc- 
tion. . 

Azimuth  correction. 

ft-  10° 

A-  20° 

ft-  30° 

ft-  40° 

ft=50° 

ft-  60° 

ft-  70° 

Jan.    1 

16  18          16  33 

17  21 

18  49 

21  17 

25  21 

3236 

47  40 

Feb.  1 

16  16 

16  31 

17  19 

1847 

21  14 

25  18 

32  32 

47  34 

Mar.  1 

16  10 

16  25 

17  12 

18  40          21  06 

25  09 

32  20 

47  16 

Apr.  1 

1602 

16  17 

17  04 

18  31 

2056 

24  57 

3204 

4653 

May   1    !      15  54         16  09 

16  55 

18  22 

20  45 

24  44 

31  48 

46  29 

June  1 
July   1 

15  48 
15  46 

16  03 
16  01 

16  49 
16  47 

18  15 
18  12 

20  38 
2035 

24  35 
24  32 

31  36 
31  32 

46  12 
4606 

Aug.  1 

15  47 

16  02 

16  48 

18  13 

2036 

24  33 

31  34 

4609 

Sept.  1 

15  53 

1608 

1654 

18  20 

2044 

24  43 

31  46 

46  26 

Oct.    1 

16  01 

16  16 

1703 

18  30 

2054 

24  55 

3202 

46  50 

Nov.  1 

1609 

16  24 

17  11 

18  39 

21  05 

25  07 

32  18 

47  13 

Dec.   1 

16  15 

1630 

17  18 

1846 

21  13 

25  17 

3230 

47  31 

TABLE  III. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
2  sin* 


t 

0" 

1m 

2m 

> 

4m 

5m 

6m 

7m 

8. 

0 

0 

2 

8 

18 

31 

49 

71 

96 

10 

0 

3 

9 

20 

34 

52 

75 

101 

20 

0 

3 

11 

22 

37 

56 

79 

106 

30 

0 

4 

12 

24 

40 

59 

83 

110 

40 

1 

5 

14 

26 

43 

63 

87 

115 

50 

1 

7 

16 

29 

46 

67 

92 

120 

60 

2 

8 

18 

31 

49 

71 

96 

126 

t 

8"° 

9m 

10" 

Urn 

12* 

13m 

14m 

15m 

9. 

„ 

„ 

n 

a 

n 

// 

„ 

„ 

0 

126 

159 

196 

238 

283 

332 

385 

442 

10 

131 

165 

203 

245 

291 

340 

394 

452 

20 

136 

171 

210 

252 

299 

349 

403 

461 

30 

142 

177 

216 

260 

307 

358 

413 

472 

40 

147 

183 

223 

267 

315 

367 

422 

482 

50 

153 

190 

230 

275 

323 

376 

432 

492 

60 

159 

196 

238 

289 

332. 

385 

442 

502 

TABLES. 


121 


TABLEN  IV. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
A = cos  3  cos  <f>  cosec  C. 


s 

5° 

6° 

7° 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

% 

8.23° 

1.95 

1.89 

1.83 

1.77 

1.72 

1.66 

1.62 

1.57 

1.53 

1.48 

1.44 

S.23° 

22 

2.03 

1.96 

1.90 

1.84 

1.  78  j  1.  72 

1.67 

1.62 

1.58 

1.53 

1.49 

22 

21 

2.12 

2.05 

1.97 

1.91 

1.84 

1.79 

1.73 

1.68 

1.63 

1.  58  1.  53 

21 

20 

2.22 

2.13 

2.05 

1.98 

1.92 

1.85 

1.79 

1.73 

1.68 

1.  63  1.  58 

20 

19 

2.32 

2.22 

2.14 

2.06 

1.99 

1.92 

1.86 

1.80 

1.74 

1.68  1.63 

19 

18 

2.42 

2.33 

2.23 

2.15 

2.06 

2.00 

1.93 

1.86 

1.80 

1.74  1.69 

18 

17 

2.54 

2.43 

2.33 

2.24 

2.15 

2.07 

2.00 

1.93 

1.86 

1.80  i  1.74 

17 

16 

2.67 

2.55 

2.44 

2.34 

2.25 

2.16 

2.08 

2.00 

1.93 

1.87 

1.80 

16 

15 

2.81 

2.68 

2.56 

2.45 

2.35 

2.25 

2.16 

2.08 

2.00 

1.93 

1.87 

15 

14 

2.97 

2.81 

2.69 

2.56 

2.45 

2.35 

2.25 

2.17 

2.08 

2.01  1.93 

14 

13 

3.14 

2.98 

2.83 

2.69 

2.57 

2.46 

2.35 

2.26 

2.17 

2.08 

2.00 

13 

12 

3.33 

3.15 

2.98 

2.83 

2.70 

2.57 

2.46 

2.35 

2.26 

2.17 

2.08 

12 

11 

3.55 

3.34 

3.15 

2.99 

2.83 

2.70 

2.57 

2.46 

2.35 

2.25 

2.16 

11 

10 

3.79 

3.55 

3.34 

3.16 

2.99 

2.84 

2.70 

2.57 

2.46 

2.35 

2.25 

10 

9 

4.07 

3.80 

3.56 

3.35 

3.16 

2.99 

2.83 

2.70 

2.57 

2.45 

2.35 

9 

8 

4.39 

4.07 

3.80 

3.56 

3.35 

3.16 

2.99 

2.83 

2.69 

2.56 

2.45 

8 

7 

4.76 

4.39 

4.07 

3.80 

3.56 

3.34 

3.15 

2.98 

2.83 

2.69 

2.56 

7 

6 

5.19 

4.76 

4.39 

4.07 

3.80 

3.55 

3.34 

3.15 

2.98 

2.81 

2.68 

6 

5 

5.71 

5.19 

4.76 

4.39 

4.07 

3.79 

3.55 

3.33 

3.14 

2.97 

2.81 

5 

4 

6.35 

5.71 

5.19 

4.75 

4.38 

4.07 

3.78 

3.54 

3.32 

3.13 

2.96 

4 

3 

7.15 

6.35 

5.71 

5.18 

4.74 

4.37 

4.05 

3.77 

3.53 

3.31 

3.12 

3 

2 

8.17 

7.14 

6.34 

5.70 

5.17 

4.73 

4.36 

4.04 

3.76 

3.52 

3.30 

2 

S.  1 

9.53 

8.16 

7.13 

6.33 

5.69 

5.16 

4.72 

4.35 

4.04 

3.75 

3.50 

S.  1 

0 

9.51 

8.14 

7.12 

6.31 

5.67 

5.14 

4.70 

4.33 

4.01 

3.73 

0 

N.  1 

9.49 

8.12 

7.10 

6.29 

5.65 

5.13 

4.69 

4.31 

3.99 

N.I 

2 

9.47 

8.10 

7.07 

6.27 

5.63 

5.10 

4.66 

4.29 

2 

3 

9.44 

8.07 

7.04 

6.24 

5.60 

5.08 

4.64 

3 

4 

9.41 

8.04 

7.01 

6.21 

5.57 

5.05 

4 

5 

9.36 

8.00 

6.97 

6.18 

5.54 

5 

6 

9.31 

7.95 

6.93 

6.14 

6 

7 

9.25 

7.90 

6.89 

7 

8 

9.19 

7.85 

8 

9 

9.13 

9 

10 

10 

11 

9.36 

1 

11 

12 

8.00 

9.31 

12 

13 

6.97 

7.95 

9.25 

13 

14 

6.18 

6.93 

7.90 

9.19 

14 

15 

5.54 

6.14 

6.89 

7.85 

9.13 

15 

16 

5.02 

5.51 

6.  10  6.  84 

7.79 

9.06 

16 

17 

4.58 

4.98 

5.47 

6.05 

6.79 

7.73 

8.98 

17 

18 

4.21 

4.55 

4.95 

5.42 

6.00 

6.73 

7.66 

8.90 

18 

19 

3.89 

4.18 

4.51 

4.91 

5.38 

5.95 

6.67 

7.59 

8.81 

19 

20 

3.62 

3.86 

4.15 

4.48 

4.86 

5.33 

5.90 

6.60 

7.51 

8.72 

20 

21 

3.37 

3.59 

3.  83  4.  11 

4.43 

4.82 

5.28 

5.84 

6.54 

7.43 

8.  63    21 

22 

3.16 

3.35 

3.  56  3.  80 

4.07 

4.39 

4.77 

5.22 

5.78 

6.46 

7.35    22 

N.23 

2.97 

3.13 

3.31 

3.52 

3.76 

4.03 

4.35 

4.72 

5.18 

5.71 

6.39  N.23 

122 


DIRECTIONS   FOR  MAGNETIC    MEASUREMENTS. 


TABLE  IV— Continued. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
A— cos  d  cos  <£  cosec  C- 


y 

1\ 

15° 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

24° 

25° 

% 

S.23° 

.44 

.41 

1.37 

1.33 

1.30 

1.27 

1.24 

1.21 

1.18 

1.15 

.12 

S.23° 

22 

.49 

.45 

1.41 

1.37 

1.33 

1.30 

1.27 

1.24 

1.21 

1.18 

.15 

22 

21 

.53 

.49 

1.45 

1.41^ 

1.37 

1.33 

1.30 

1.27 

1.24 

1.21 

.18 

21 

20 

.58 

.53 

1.49 

1.45 

1.41 

1.37 

1.33 

1.30 

1.27 

1.24 

.20 

20 

19 

.63 

.58 

1.53 

1.49 

1.45 

1.41 

1.37 

1.33 

1.30 

1.27 

.23 

19 

18 

.69 

1.63 

1.59 

1.53 

1.49 

1.45 

1.41 

1.37 

1.33 

1.30 

.26 

18 

17 

.74 

1.69 

1.64 

1.59 

1.53 

1.49 

1.45 

1.41 

1.37 

1.33 

.30 

17 

16 

.80 

1.74 

1.69 

1.63 

1.58 

1.53 

1.49 

1.45 

1.41 

1.37 

.33 

16 

15 

1.87 

1.80 

1.74 

1.69 

1.63 

1.58 

1.53 

1.49 

1.44 

1.41 

.36 

15 

14 

1.93 

1.87 

1.80 

1.74 

1.68 

1.63 

1.58 

1.53 

1.48 

1  44 

.40 

14 

13 

2.00 

1.93 

1.86 

1.80 

1.74 

1.68 

1.63 

1.58 

1.53 

1.48 

.43 

13 

12 

2.08 

2.00 

1.93 

1.86 

1.80 

1.73 

1.68 

1.62 

1.57 

1.53 

.47 

12 

11 

2.16 

2.08 

2.00 

1.93 

1.86 

1.79 

1.73 

1.67 

1.62 

1.57 

.51 

11 

10 

2.25 

2.16 

2.07 

2.00 

1.92 

1.85 

1.79 

1.72 

1.66 

1.62 

.56 

10 

9 

2.35 

2.25 

2.15 

2.06 

1.99 

1.92 

1.84 

1.78 

1.72 

1.66 

.60 

9 

8 

2.45 

2.34 

2.24 

2.15 

2.06 

1.98 

1.91 

1.84 

1.77 

1.71 

.65 

8 

7 

2.56 

2.44 

2.33 

2.23 

2.14 

2.05 

1.97 

1.90 

1.83 

1.76 

.70 

7 

6 

2.68 

2.55 

2.43 

2.33 

2.22 

2.13 

2.05 

1.96 

1.89 

1.82 

.75 

6 

5 

2.81 

2.67 

2.54 

2.42 

2.32 

2.22 

2.12 

2.03 

1.95 

1.88 

.81 

5 

4 

2.96 

2.80 

2.66 

2.53 

2.41 

2.30 

2.20 

2.11 

2.02 

1.94 

.87 

4 

3 

3.12 

2.95 

2.79 

2.65 

2.52 

2.40 

2.29 

2.19 

2.10 

2.01 

.93 

3 

2 

3.30 

3.10 

2.94 

2.78 

2.6* 

2.51 

2.39 

2.28 

2.18 

2.08 

2.00 

2 

S.  1 

3.50 

3.29 

3.09 

2.92 

2.76 

2.62 

2.49 

2.37 

2.26 

2.16 

2.07 

S.  1 

0 

3.73 

3.49 

3.27 

3.08 

2.90 

2.75 

2.61 

2.48 

2.36 

2.25 

2.14 

0 

N.I 

3.99 

3.71 

3.47 

3.25 

3.06 

2.89 

2.73 

2.59 

2.46 

2.34 

2.23 

N.  1 

2 

4.29 

3.97 

3.69 

3.45 

3.23 

3.04 

2.87 

2.71 

2.57 

2.44 

2.32 

2 

3 

4.64 

4.27 

3.95 

3.67 

3.43 

3.22 

3.02 

2.84 

2.69 

2.55 

2.42 

3 

4 

5.05 

4.61 

4.24 

3.92 

3.64 

3.40 

3.19 

2.99 

2.82 

2.66 

2.52 

4 

5 

5.54 

5.02 

4.58 

4.21 

3.89 

3.62 

3.37 

3.16 

2.97 

2.80 

2.64 

5 

6 

6.14 

5.51 

4.98 

4.55 

4.18 

3.86 

3.59 

3.35 

3.13 

2.94 

2.77 

6 

7 

6.89 

6.10 

5.47 

4.95 

4.51 

4.15 

3.83 

3.56 

3.31 

3.10 

2.91 

7 

8 

7.85 

6.84 

6.05 

5.42 

4.91 

4.48 

4.11 

3.80 

3.52 

3.28 

3.07 

8 

9 

9.13 

7.79 

6.79 

6.00 

5.38 

4.86 

4.43 

4.07 

3.76 

3.49 

3.25 

9 

10 

9.06 

7.73 

6.73 

5.95 

5.33 

4.82 

4.39 

4.03 

3.72 

3.45 

10 

11 

8.98 

7.66 

6.67 

5.90 

5.28 

4.77 

4.35 

3.99 

3.68 

11 

12 

8.90 

7.59 

6.60 

5.84 

5.22 

4.72 

4.30 

3.94 

12 

13 

8.81 

7.51 

6.54 

5.78 

5.16 

4.66 

4.25 

13 

14 

8.72 

7.43 

6.46 

5.71 

5.10 

4.61 

14 

15 

8.63 

7.35 

6.39 

5.64 

5.04 

15  • 

16 

8.53 

7.26 

6.31 

5.57 

16 

17 

8.42 

7.17 

6.23 

17 

18 

8.31 

7.07 

18 

19 

9.91 

8.20 

19 

20 

9.77 

20 

21 

8.63 

21 

22 

7.35 

8.53 

22 

N.23 

6.39 

7.26 

8.42 

X.23 

TABLES. 


123 


TABLE  IV — Continued. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
A=cosd  cos^cosec  C 


V 

25° 

26° 

27° 

28° 

29° 

30° 

31° 

32° 

33° 

34° 

35° 

y, 

S.23° 

1.12 

1.10 

1.07 

1.05 

1.02 

1,00 

0.98 

0.95 

0.93 

0.91 

0.89 

S.23° 

22 

1.15 

1.12 

1.10 

1.07 

1.04 

1.02 

1.00 

0.97 

0.95 

0.93 

0.91 

22 

21 

1.18 

1.15 

1.12 

1.09 

1.07 

1.04 

1.02 

0.99 

0.97 

0.94 

0.92 

21 

20 

1.20 

1.17 

1.14 

1.12 

1.09 

1.06 

1.04 

1.01 

0.99 

0.96 

0.94 

20 

19 

1.23 

1.20 

1.17 

1.14 

1.11 

1.08 

1.06 

1.03 

1.01 

0.98 

0.96 

19 

18 

1.26 

1.23 

1.20 

1.17 

1.14 

1.11 

1.08 

1.05 

1.03 

1.00 

0.98 

18 

17 

1.30 

1.26 

1.23 

1.19 

1.16 

1.13 

1.10 

1.07 

1.05 

1.02 

0.99 

17 

16 

1.33 

1.29 

1.26 

1.22 

1.19 

1.16 

1.13 

1.10 

1.07 

1.04 

1.01 

16 

15 

1.36 

1.32 

1.29 

1.25 

1.22 

1.18 

1.15 

1.12 

1.09 

1.06 

1.03 

15 

14 

1.40 

1.36 

1.32 

1.28 

1.24 

1.21 

1.18 

1.14 

1.11 

1.08 

1.05 

14 

13 

1.43 

1.39 

1.35 

1.32 

1.27 

1.24 

1.20 

1.17 

1.14 

1.10 

1.07 

13 

12 

1.47 

1.43 

1.38 

1.34 

1.30 

1.27 

1.23 

1.19 

1.16 

1.13 

1.10 

12 

11 

1.51 

1.47 

1.42 

1.38 

1.34 

1.30 

1.26 

1.22 

1.18 

1.15 

1.12 

11 

10 

1.56 

1.51 

1.46 

1.41 

1.37 

1.33 

1.29 

1.25 

1.21 

1.18 

1.14 

10 

9 

1.60 

1.55 

1.50 

1.45 

1.40 

1.36 

1.32 

1.28 

1.24 

1.20 

1.16 

9 

8 

1.65 

1.59 

1.54 

1.49 

1.44 

1.39 

1.35 

1.31 

1.27 

1.23 

1.19 

8 

7 

1.70 

1.64 

1.58 

1.53 

1.48 

1.43 

1.38 

1.34 

1.30 

1.25 

1.21 

7 

6 

1.75 

1.69 

1.C3 

1.57 

1.52 

1.46 

1.42 

1.37 

1.33 

1.28 

1.24 

6 

7 

5 

1.81 

1.74 

1.68 

1.62 

1.56 

1.50 

1.45 

1.40 

1.36 

1.31 

1.27 

5 

4 

1.87 

1.79 

1.73 

1.66 

1.60 

1.55 

1.49 

1.44 

1.39 

1.34 

1.30 

4 

3 

1.93 

1.85 

1.78 

1.71 

1.65 

1.59 

1.53 

1.48 

1.42 

1.38 

1.33 

3 

2 

2.00 

1.91 

1.84 

1.77 

1.70 

1.63 

1.57 

1.52 

1.46 

1.41 

1.36 

2 

S.   1 

2.07 

1.98 

1.90 

1.82 

1.75 

1.68 

1.62 

1.56 

1.50 

1.45 

1.39 

S.  1 

0 

2.14 

2.05 

1.96 

1.88 

1.80 

1.73 

1.66 

i.eo 

1.54 

1.48 

1.43 

0 

N.I 

2.23 

2.13 

2.03 

1.95 

1.86 

1.79 

1.71 

1.65 

1.58 

1.52 

1.47 

N.  1 

2 

2.32 

2.21 

2.11 

2.01 

1.93 

1.84 

1.77 

1.69 

1.63 

1.56 

1.50 

2 

3 

2.42 

2.30 

2.19 

2.09 

1.99 

1.91 

1.82 

1.75 

1.68 

1.61 

1.54 

3 

4 

2.52 

2.39 

2.27 

2.17 

2.06 

1.97 

1.88 

1.80 

1.73 

1.65 

1.59 

4 

5 

2.64 

2.50 

2.37 

2.25 

2.14 

2.04 

1.95 

1.86 

1.78 

1.70 

1.63 

5 

6 

2.77 

2.61 

2.47 

2.34 

2.23 

2.12 

2.02 

1.92 

1.84 

1.76 

1.68 

6 

7 

2.91 

2.74 

2.59 

2.44 

2.32 

2.20 

2.09 

1.99 

1.90 

1.81 

1.73 

7 

8 

3.07 

2.88 

2.71 

2.56 

2.42 

2.29 

2.17 

2.06 

1.97 

1.87 

1.79 

8 

9 

3.25 

3.04 

2.85 

2.68 

2.53 

2.39 

2.26 

2.14 

2.04 

1.94 

1.85 

9 

10 

3.45 

3.21 

3.00 

2.81 

2.65 

2.49 

2.36 

2.23 

2.11 

2.01 

1.91 

10 

11 

3.68 

3.41 

3.17 

2.96 

2.78 

2.61 

2.46 

2.32 

2.20 

2.08 

1.98 

11 

12 

3.94 

3.63 

3.37 

3.13 

2.93 

2.74 

2.58 

2.43 

2.29 

2.17 

2.05 

12 

13 

4  ?5 

3.90 

3.59 

3.32 

3.09 

2.89 

2.70 

2.54 

2.39 

2.25 

?  13 

13 

14 

4.61 

4.19 

3.84 

3.54 

3.28 

3.05 

2.85 

2.66 

2.50 

2.35 

2.22 

14 

15 

5.04 

4.55 

4.14 

3.79 

3.49 

3.23 

3.00 

2.80 

2.62 

2.46 

2.31 

15 

16 

5.57 

4.98 

4.49 

4.08 

3.74 

3.44 

3.18 

2.96 

2.76 

2.58 

2.42 

16 

17 

6.23 

5.49 

4.91 

4.43 

4.02 

3.68 

3.39 

3.13 

2.91 

2.71 

2.54 

17 

18 

7.07 

6.14 

5.42 

4.84 

4.36 

3.96 

3.62 

3.33 

3.08 

2.86 

2.66 

18 

19 

8.20 

6.97 

6.05 

5.34 

4.76 

4.29 

3.90 

3.56 

3.28 

3.03 

2.81 

19 

20 

9.77 

8.08 

6.87 

5.96 

5.25 

4.69 

4.22 

3.83 

3.50 

3.22 

2.97 

20 

21 

9.63 

7.96 

6.76 

5.87 

5.17 

4.61 

4.15 

%3.77 

3.44 

3.16 

21 

22 

9.48 

7.83 

6.65 

5.77 

5.08 

4.53 

4.07 

3.70 

3.38 

22 

N.23 

9.32 

7.71 

6.54 

5.67 

4.99 

4.45 

4.00 

3.63 

N.23 

124 


DIRECTIONS   FOR  MAGNETIC   MEASUREMENTS. 


TABLE  IV — Continued. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
A=cos  d  cos#  cosec  } 


X 

35° 

36° 

37° 

38° 

39° 

40° 

41° 

42° 

43° 

44° 

45° 

J7 
/  * 

8.23° 

0.89 

0.87 

0.85 

0.83 

0.81 

0.79 

0.77 

0.75 

0.74 

0.72 

0.70 

8.23° 

22 

0.91 

0.88 

0.86 

0.84 

0.82 

0.80 

0.78 

0.77 

0.75 

0.73 

0.71 

22 

21 

0.92 

0.90 

0.88 

0.86 

0.84 

0.82 

0.80 

0.78 

0.76 

0.74 

0.72 

21 

20 

0.94 

0.92 

0.90 

0.87 

0.85 

0.83 

0.81 

0.79 

0.77 

0.75 

0.73 

20 

19 

0.96 

0.93 

0.91 

0.89 

0.87 

0.84 

0.82 

0.80 

0.78 

0.76 

0.74 

19 

18 

0.98 

0.95 

0.93 

0.90 

0.88 

0.86 

0.84 

0.82 

0.80 

0.78 

0.76 

18 

17 

0.99 

0.97 

0.94 

0.92 

0.90 

0.87 

0.85 

0.83 

0.81 

0.79 

0.77 

1- 

16 

1.01 

0.99 

0.96 

0.94 

0.91 

0.89 

0.86 

0.84 

0.82 

0.80' 

0.78 

16 

15 

1.03 

1.01 

0.98 

0.95 

0.93 

0.90 

0.88 

0.86 

0.83 

0.81 

0.79 

15 

14 

1.05 

1.03 

1.00 

0.97 

0.94 

0.92 

0.89 

0.87 

0.85 

0.82 

0.80 

14 

13 

1.07 

1.05 

1.02 

0.99 

0.96 

0.93 

0.91 

0.88 

0.86 

0.84 

0.81 

13 

12 

1.10 

1.07 

1.04 

1.01 

0.98 

0.95 

0.92 

0.90 

0.87 

0.85 

0.82 

12 

11 

1.12 

1.09 

1.06 

1.02 

1.00 

0.97 

0.94 

0.91 

0.89 

0.86 

0.84 

11 

10 

1.14 

1.11 

1.08 

1.04 

1.01 

0.98 

0.96 

0.93 

0.90 

0.88 

0.85 

10 

9 

1.16 

1.13 

1.10 

1.06 

1.03 

1.00 

0.97 

0.94 

0.92 

0.89 

0.86 

9 

8 

1.19 

1.15 

1.12 

1.08 

1.05 

1.02 

0.99 

0.96 

0.93 

0.90 

0.88 

8 

7 

1.21 

1.18 

1.14 

1.11 

1.07 

1.04 

1.01 

0.98 

0.95 

0.92 

0.89 

7 

6 

1.24 

1.20 

1.17 

1.13 

1.09 

1.06 

1.03 

0.99 

0.96 

0.93 

0.91 

6 

5 

1.27 

1.23 

1.19 

1.15 

1.11 

1.08 

1.04 

1.01 

0.98 

0.95 

IX  99 

5 

4 

1.30 

1.26 

1.21 

1.17 

1.14 

1.10 

1.07 

1.03 

1.00 

0.97 

0.94 

4 

3 

1.33 

1.28 

1.24 

1.20 

1.16 

1.12 

1.09 

1.05 

1.02 

0.98 

0.95 

3 

2 

1.36 

1.31 

1.27 

1.23 

1.18 

1.14 

1.11 

1.07 

1.03 

1.00 

0.97 

2 

S.  1 

1.39 

1.34 

1.30 

1.25 

1.21 

1.17 

1.13 

1.09 

1.05 

1.02 

0.98 

S.  1 

0 

1.43 

1.38 

1.33 

1.28 

1.24 

1.19 

1.15 

1.11 

1.07 

1.04 

1.00' 

0 

N.I 

1.47 

1.41 

1.36 

1.31 

1.26 

1.22 

1.17 

1.13 

1.09 

1.05 

1.02 

N.  1 

2 

1.50 

1.45 

1.39 

1.34 

1.29 

1.24 

1.20 

1.16 

1.11 

1.07 

1.04 

2 

3 

1.54 

1.48 

1.43 

1.37 

1.32 

1.27 

1.22 

1.18 

1.14 

1.09 

1.06 

3 

4 

1.59 

1.52 

1.46 

1.41 

1.35 

1.30 

1.25 

1.20 

1.16 

1.12 

1.07 

4 

5 

1.63 

1.56 

1.50 

1.44 

1.38 

1.33 

1.28 

1.23 

1.18 

1.14 

1.10 

5 

•   6 

1.68 

1.61 

1.54 

1.48 

1.42 

1.36 

1.31 

1.26 

1.21 

1.16 

1.12 

6 

7 

1.73 

l!66 

1.58 

1.52 

1.46 

1.40 

1.34 

1.29 

1.23 

1.19 

1.14 

7 

8 

1.79 

1.71 

1.63 

1.56 

1.49 

1.43 

1.37 

1.32 

1.26 

1.21 

1.16 

8 

9 

1.85 

1.76 

1.68 

1.60 

1.54 

1.47 

1.41 

1.35 

1.29 

1.24 

1.19 

9 

10 

1.91 

1.82 

1.73 

1.65 

1.58 

.51 

1.44 

1.38 

1.32 

1.27 

1.21 

10 

11 

1.98 

1.88 

1.79 

1.70 

1.63 

.55 

1.48 

1.42 

1.35 

1.30 

1.24 

11 

12 

2.05 

1.95 

1.85 

1.76 

1.67 

.60 

1.52 

1.45 

1.39 

1.33 

1.27 

12 

13 

2.13 

2.02 

1.91 

1.82 

1.73 

.64 

1.57 

1.49 

1.43 

1.36 

1.30 

13 

14 

2.22 

2.10 

1.98 

1.88 

1.78 

.70 

1.61 

1.54 

1.46 

1.40 

1.33 

14 

15 

2.31 

2.18 

2.06 

1.95 

1.85 

.75 

1.66 

1.58 

1.51 

1.43 

1.37 

15 

16 

2.42 

2.27 

2.14 

2.02 

1.91 

.81 

1.72 

1.63 

1.55 

1.47 

1.40 

16 

17 

2."54 

2.38 

2.23 

2.10 

1.98 

.88 

1.77 

1.68 

1.60 

1.51 

1.44 

17 

18 

2.66 

2.49 

2.33 

2.19 

2.06 

.94 

1.84 

1.74 

1.65 

1.56 

1.48 

18 

19 

2.81 

2.62 

2.44 

2.29 

2.15 

2.02 

1.90 

1.80 

1.70 

1.61 

1.52 

19 

20 

2.97 

2.76 

2.57 

2.40 

2.24 

2.10 

1.98 

1.86 

1.76 

1.66 

1.57 

20 

21 

3.16 

2.92 

2.70 

2.52 

2.35 

2.20 

2.06 

1.94 

1.82 

1.72 

1.62 

21 

22 

3.38 

3.10 

2.86 

2.65 

2.46 

2.30 

2.15 

2.01 

1.89 

1.78 

1.68 

22 

N.23 

3.63 

3.31 

3.04 

2.80 

2.60 

2.41 

2.25 

2.10 

1.97 

1.85 

1.74 

N.23 

TABLES. 


125 


TABLE  IV— Continued. 

Latitude  from  circum-meridian  altitudes  of  the  sun. 
.4= cos  d  cos  4>  cosec  C 


V 

»\ 

45° 

46° 

47° 

48° 

49° 

50° 

55° 

60° 

65° 

70° 

*/ 
/* 

.8.23° 

0.70 

0.69 

0.67 

0.65 

0.64 

0.62 

0.54 

0.46 

0.39 

8.23° 

22 

0.71 

0.69 

0.68 

0.66 

0.64 

0.63 

0.55 

0.47 

0.39 

22 

21 

0.72 

0.71 

0.69 

0.67 

0.65 

0.63 

0.55 

0.47 

0.40 

21 

20 

0.73 

0.71 

0.70 

0.68 

0.66 

0.64 

0.56 

0.48 

0.40 

20 

19 

0.74 

0.72 

0.71 

0.69 

0.67 

0.65 

0.56 

0.48 

0.40 

0.32 

19 

18 

0.76 

0.74 

0.72 

0.70 

0.68 

0.66 

0.57 

0.49 

0.40 

0.33 

18 

17 

0.77 

0.75 

0.73 

0.71 

0.69 

0.67 

0.58 

0.49 

0.41 

0.33 

17 

16 

0.78 

0.76 

0^74 

0.72 

0.70 

0.68 

0.58 

0.50 

0.41 

0.33 

16 

15 

0.79 

0.77 

0.75 

0.73 

0.70 

0.69 

0.59 

0.50 

0.41 

0.33 

15 

14 

0.80 

0.78 

0.76 

0.74 

0.71 

0.69 

0.60 

0.50 

0.42 

0.33 

14 

13 

0.81 

0.79 

0.77 

0.75 

0.72 

0.70 

0.60 

0.51 

0.42 

0.34 

13 

12 

0.82 

0.80 

0.78 

0.76 

0.73 

0.71 

0.61 

0.51 

0.42 

0.34 

12 

11 

0.84 

0.81 

0.79 

0.77 

0.74 

0.72 

0.62 

0.52 

0.43 

0.34 

11 

10 

0.85 

0.82 

0.80 

0.78 

0.75 

0.73 

0.62 

0.52 

0.43 

0.34 

10 

9 

0.86 

0.84 

0.81 

0.79 

0.76 

0.74 

0.63 

0.53 

0.43 

0.34 

9 

8 

0.88 

0.85 

0.82 

0.80 

0.78 

0.75 

0.64 

0.53 

0.44 

0.35 

8 

7 

0-89 

0.86 

0.84 

0.81 

0.78 

0.76 

0.64 

0.54 

0.44 

0.35 

7 

6 

0.91 

0.88 

0.85 

0.82 

0.80 

0.77 

0.65 

0.54 

0.44 

0.35 

6 

5 

0.92 

0.89 

0.86 

0.83 

0.81 

0.78 

0.66 

0.55 

0.45 

0.35 

5 

4 

0.94 

0.90 

0.88 

0.85 

0.82 

0.79 

0.67 

0.55 

0.45 

0.35 

4 

3 

0.95 

0.92 

0.89 

0.86 

0.83 

0.80 

0.68 

0.56 

0.46 

0.36 

3 

2 

0.97 

0.93 

0.90 

0.87 

0.84 

0.82 

0.68 

0.57 

0.46 

0.36 

2 

S.I 

0.98 

0.95 

0.92 

0.89 

0.86 

0.83 

0.69 

0.57 

0.46 

0.36 

S.  1 

0 

1.00 

0.97 

0.93 

0.90 

0.87 

0.84 

0.70 

0.58 

0.47 

0.36 

0 

N.  1 

1.02 

0.98 

0.95 

0.92 

0.88 

0.85 

0.71 

0.58 

0.47 

0.37 

N.  1 

2 

1.04 

1.00 

0.96 

0.93 

0.90 

0.86 

0.72 

0.59 

0.47 

0.37 

2 

3 

1.06 

1.02 

0.98 

0.94 

0.91 

0.88 

0.73 

0.60 

0.48 

0.37 

3 

4 

1.07 

1.04 

0.99 

0.96 

0.93 

0.89 

0.74 

0.60 

0.48 

0.37 

4 

5 

1.10 

1.05 

1.02 

0.98 

0.94 

0.91 

0.75 

0.61 

0.48 

0.38 

5 

6 

1.12 

1.07 

1.03 

0.99 

0.96 

0.92 

0.76 

0.61 

0.49 

0.38 

6 

7 

1.14 

1.10 

1.05 

1.01 

0.97 

0.94 

0.77 

0.62 

0.49 

0.38 

7 

8 

1.16 

1.12 

1.07 

1.03 

0.99 

0.95 

0.78 

0.63 

0.50 

0.38 

8 

9 

1.19 

1.14 

1.09 

1.05 

1.01 

0.97 

0.79 

0.64 

0.50 

0.39 

9 

10 

1.21 

1.16 

1.12 

1.07 

1.03 

0.98 

0.80 

0.64 

0.51 

0.39 

10 

11 

1.24 

1.19 

1.14 

1.09 

1.05 

1.00 

0.81 

0.65 

0.51 

0.39 

11 

12 

1.27 

1.22 

1.16 

1.11 

.07 

1.02 

0.82 

0.66 

0.52 

0.39 

12 

13 

1.30 

1.24 

1.19 

1.14 

.09 

1.04 

0.84 

0.67 

0.52 

0.40 

13 

14 

1.33 

1.27 

1.22 

1.16 

.11 

1.06 

0.85 

0.67 

0.53 

0.40 

14 

15 

1.37 

1.30 

1.24 

1.19 

.13 

1.08 

0.86 

0.68 

0.53 

0.40 

15 

16 

1.40 

1.34 

1.27 

1.21 

.16 

1.10 

0.88 

0.69 

0.54 

0.41 

16 

17 

1.44 

1.37 

1.30 

1.24 

.18 

1.13 

0.89 

0.70 

0.54 

0.41 

17 

18 

1.48 

1.41 

1.34 

1.27 

.21 

1.15 

0.91 

0.71 

0.55 

0.41 

18 

19 

1.52 

1.45 

1.37 

1.31 

.24 

1.18 

0.92 

0.72 

0.56 

0.42 

19 

20 

1.57 

1.49 

1.41 

1.34 

1.27 

1.21 

0.94 

0.73 

0.56 

0.42 

20 

21 

1.62 

1.53 

1.45 

1.38 

1.30 

1.24 

0.96 

0.74 

0.57 

0.46 

21 

22 

1.68 

1.58 

1.50 

1.41 

1.34 

1.27 

0.98 

0.75 

0.57 

0.50 

22 

N.23 

1.74 

1.64 

1.54 

1.46 

1.38 

1.30 

1.00 

0.76 

0.58 

0.54 

N.23 

126  DIRECTIONS   FOE  MAGNETIC   MEASUREMENTS. 

TABLE  V. 

Correction  for  rate  of  chronometer  (oscillations). 
(The  correction  is  to  be  added  when  chronometer  was  losing  and  subtracted  when  gaining.) 


Daily 
rate. 

Time  of  one  oscillation. 

3».0 

4».0 

5».0 

6».0 

7».0 

8».0 

9».0 

s. 

*. 

s. 

*. 

s. 

0. 

*. 

*. 

1.0 

0.00003 

0.00005 

0.00006 

0.00007 

0.00008 

0.00009 

0.00010 

2.0 

07 

09 

12 

14 

16 

19 

21 

3.0 

10 

14 

17     ,               21 

24 

28 

31 

4.0 

14 

19 

23 

28 

32 

37 

42 

5.0 

17 

23 

29 

35 

41 

46 

52 

6.0 

21 

28 

35 

42 

49 

56 

63 

7.0 

24 

32 

40 

49 

57 

65 

73 

8.0 

28 

37 

46 

56 

65 

74 

83 

9.0 

31 

42 

52 

62 

73 

83 

94 

10.0 

35 

46 

58 

69 

81 

93 

104 

20.0 

69 

93 

116 

139 

162 

185 

'       208 

30.0 

0.00104 

0.00139 

0.  00174 

0.00208 

0.  00243 

0.  00278 

0.  00313 

3m56'.6 

0.00821 

0.  01095 

0.  01369 

0.01643 

0.  01917 

0.  02190 

0.  02464 

The  last  line  is  added  for  the  case  in  which  a  sidereal  chronometer  was  used  in  observing. 

TABLE  VI. 
Torsion  factor  (oscillations). 

(Values  of  [log  5400-log  (5400-ft)]  are  given  in  units  of  the  fifth  decimal 
place;  h  is  expressed  in  minutes  of  arc.) 


A 

0.0 

0.1 

0.2 

0.3 

0.4' 

0.5 

0.6 

0.7 

0.8 

... 

0 

0 

1 

2 

2 

3 

4 

5 

6 

*6 

7 

1 

8 

9 

10 

10 

11 

12 

13 

14 

14 

15 

2 

16 

17 

18 

18 

19 

20 

21 

22 

23 

23 

3 

24 

25 

26 

27 

27 

28 

29 

30 

31 

31 

4 

32 

33 

34 

35 

35 

36 

37 

38 

39 

39 

5 

40 

41 

42 

43 

43 

44 

45 

46    47 

47 

6 

48 

49 

50 

51 

51 

52 

53 

54 

55 

55 

7 

56 

57 

58 

59 

59 

60 

61 

62 

63 

63 

8 

64 

65 

66 

67 

68 

68 

69 

70 

71 

72 

9 

72 

73 

74 

75 

76 

76 

77 

78 

79 

80 

TABLES. 


127 


TABLE  VII. 

Reduction  of  log  C 'from  20°  C.  to  other  temperatures  (deflections). 
(The  corrections  are  given  in  terms  of  the  fifth  decimal  place  in  the  logarithm.) 


Temp. 

Corr'n. 

Temp. 

Corr'n. 

Temp. 

Corr'n. 

Temp. 

Corr'n. 

0 

0 

0 

0 

0 

+50 

10 

+25 

20 

0 

30 

-25 

1 

47.5 

11 

22.  5 

21 

-  2.5 

31 

27.5 

2 

45                12 

20 

22 

5 

32 

30. 

3 

42.5 

13 

17.5 

23 

7.5 

33 

32.5 

4 

40                 14 

15 

24 

10 

34 

35 

5 

37.5              15 

12.5 

25 

12.5 

35 

37.5 

6 

35                 16 

10 

26 

15 

36 

40 

7 

32.5 

17 

7.5     ! 

27 

17.5 

37 

42.5 

8 

30 

18 

5 

28            20 

38 

45 

9 

27.5 

19 

+  2.5 

29 

22.5 

39 

47.5 

10 

+25 

20 

0 

30 

-25 

40 

-60 

TABLE  VIII. 
Correction  for  lack  of  balance  of  dip  needle. 

(dl  is  the  difference  of  the  two  values  of  dip  from  observations  before  and  after 
reversal  of  polarities.    The  correction  is  always  to  be  added.) 


7 

10° 

20° 

30° 

40° 

45° 

50° 

55° 

60° 

65° 

70° 

75° 

dl 

0  10 

0.00 

0.00 

0.00 

0.00 

0.01 

0.01 

0.01 

0.01 

0.02 

0.03 

0.03 

20 

0.00 

0.02  0.03 

0.03 

0.03 

0.04 

0.04 

0.05 

0.06 

0.08 

0.11 

30 

0.00 

0.03 

0.04 

0.05 

0.06 

0.08 

0.09 

0.11 

0.14 

0.18 

0.24 

40 

0.01 

0.05 

0.06 

0.09 

0.11 

0.14 

0.16 

0.20 

0.25 

0.32 

0.43 

50 

0.02 

0.08 

0.10 

0.15 

0.18 

0.22 

0.26 

0.31 

0.40 

0.50 

0.67 

1  00 

0.03 

0.10 

0.15 

0.22 

0.27 

0.32 

0.38 

0.45 

0.56 

0.72 

0.97 

10 

0.05 

0.  13  0.  20 

0.30 

0.36 

0.43 

0.51 

0.62 

0.76 

0.98 

1.33 

20 

0.07 

0.17  0.26  0.39 

0.47 

0.56 

0.67 

0.81 

0.99 

1.28 

1.74 

30 

0.09 

0.22 

0.33 

0.49 

0.59 

0.70 

0.85 

1.03 

1.26 

1.62 

2.20 

40 

0.12 

0.27 

0.41 

0.60 

0.73 

0.86 

1.05 

1.27 

1.56 

2.00 

2.71 

50 

0.15 

0.33 

0.50 

0.73 

0.88 

1.04 

1.26 

1.54 

1.89 

2.42 

3.28 

2  00 

0.17 

0.  39  0.  60 

0.87 

1.05 

1.24 

1.50 

1.82 

2.25 

2.88 

3.91 

128  DIRECTIONS   FOE  MAGNETIC    MEASUREMENTS. 

TABLE  IX. 
Diurnal  variation  of  declination. 


Month. 

Jan.,  Feb.,  Nov.,  Dec. 

Mar.,  Apr.,  Sept.,  Oct. 

May,  June,  July,  Aug. 

Hour. 

Sitka. 

Ch. 

Hon. 

P.  R. 

Sitka. 

Ch. 

Hon. 

P.  R. 

Sitka. 

Ch. 

Hon. 

P.  R. 

1 

-0.3 

-0.2 

-0.2 

--0.2 

-0.2 

+0.2 

-0.2 

-0.2 

-0.8 

+0.1 

-0.1 

-0.2 

2 

-0.1 

-0.2 

-0.1 

-0.3 

-0.1 

+0.3 

-0.1 

-0.2 

-0.6 

+0.2 

0.0 

-0.1 

3 

0.0 

-0.1 

-0.1 

-0.3 

+0.2 

+0.6 

0.0 

-0.1 

-0.2 

+0.4 

+0.2 

0.0 

4 

+0.1 

+0.1 

0.0 

-0.2 

+0.4 

+0.8 

+0.2 

+0.1 

+0.9 

+0.8 

+0.4 

+0.2 

5 

+0.3 

+0.3 

+0.1 

-0.1 

+1.1 

+1.1 

+0.4 

+0.3 

+2.6 

+1.8 

+0.7 

+0.6 

6 

+0.5 

+0.6 

0.0 

0.0 

+2.1 

+1.9 

+0.9 

+0.8 

+4.5 

+3.5 

+1.9 

+1.8 

7 

+1.0 

+1.1 

0.0 

+0.1 

+3.4 

+3.3 

+2.2 

+2.0 

+6.2 

+5.0 

+3.6 

+3.4 

8 

+1.7 

+2.1 

+1.0 

+1.1 

+4.7 

+4.2 

+3.1 

+2.6 

+7.2 

+5.3 

+3.5 

+3.G 

9 

+2.2 

+2.9 

+1.9 

+2.3 

+4.7 

+3.6 

+2.7 

+2.5 

+0.8 

+3.9 

+2.1 

+2.5 

10 

+1.8 

+2.3 

+2.0 

+2.8 

+3.6 

+1.7 

+1.3 

+1.8 

+4.4 

+0.9 

+0.2 

+1.0 

11 

+1.0 

+0.5 

+0.9 

+2.1 

+1.7 

-1.0 

-0.4 

+0.6 

+0.8 

-2.2 

-1.5 

-0.4 

12 

+0.1 

-1.6 

-0.5 

+0.5 

-0.5 

-3.2 

-1.7 

-0.6 

-2.0 

-4.3 

-2.5 

-1.3 

13 

-0.7 

-2.8 

-1.4 

-0.8 

-2.3 

-4.2 

-2.1 

-1.5 

-3.8 

-5.0 

-2.5 

-1.9 

14 

-1.5 

-2.8 

-1.8 

-1.5 

-3.0 

-4.0 

-1.9 

-2.0 

-5.0 

-4.6 

-2.0 

-2.1 

15 

-1.6 

-2.1 

-1.5 

-1.7 

-3.3 

-3.0 

-1.4 

-1.9 

-5.3 

-3.4 

-1.3 

-1.9 

16 

-1.5 

-1.4 

-0.9 

-1.4 

-3.1 

-1.7 

-0.8 

-1.4 

-4.6 

-2.0 

-0.7 

-1.4 

17 

-1.3 

-0.6 

0.0 

-1.0 

-2.6 

-0.7 

-0.5 

-0.9 

-3.5 

-0.5 

-0.4 

-0.7 

18 

-0.8 

-0.1 

+0.1 

-0.6 

-2.0 

-0.4 

-0.4 

-0.6 

-2.2 

+0.1 

-0.4 

-0.5 

19 

-0.4 

+0.  2     +0.  1 

-0.3 

-1.4 

-0.2 

-0.3 

-0.5 

-1.1 

+0.1 

-0.3 

-0.5 

20 

-0.2 

+0.4 

+0.2 

-0.1 

-0.9 

0.0 

-0.2 

-0.4 

-0.8 

-0.1 

-0.3 

-0.5 

21 

-0.2 

+0.6 

+0.1 

0.0 

-0.8 

+0.1 

-0.2 

-0.3 

-0.7 

0.0 

-0.3 

-0.5 

22 

-0.2 

+0.4        0.0 

0.0 

-0.7 

+0.2 

-0.3 

-0.2 

-0.9 

0.0 

-0.2 

-0.4 

23 

-0.2 

+0.3        0.0 

-0.1 

-0.7 

+0.2 

-0.3 

-0.2 

-0.9 

+0.1 

-0.2 

-0.3 

24 

-0.2 

+0.  1     -0.  1 

-0.2 

-0.0 

+0.2 

-0.2 

-0.2 

-0.9 

+0.1 

-0.2 

-0.2 

Sitka,  Alaska,  1902-1906.    Mean  declination,  29  56.6  E. 
Cheltenham,  Md.,  1902-1906.  5  13.9  W. 

Honolulu,  Hawaii,  1902-190K.  9  20.9  E. 

Vieques,  Porto  Rico,  1904-1906.  1  38. 4  W. 

A  plus  sign  indicates  that  e.ast  declination  is  greater  or  west  declination  is  less  than  the  mean  for  the  day. 


TABLES. 

TABLE  X. 
Diurnal  variation  of  dip. 


129 


Month. 

Jan.,  Feb.,  Nov.,  Dec. 

Mar.,  Apr.,  Sept.,  Oct. 

May,  June,  July,  Aug. 

Hour. 

Sitka. 

Ch. 

Hon. 

P.  R. 

Sitka. 

Ch. 

Hon. 

P.  R. 

Sitka. 

Ch. 

Hon. 

P.  R. 

1 

-0.2 

-0.1 

+0.6 

+0.2 

-0.4 

-0.3 

+0.6 

+0.3 

-0.4 

-0.1 

+0.4 

+0.2 

2 

-0.2 

-0.2 

+0.6 

+0.2 

-0.5 

-0.3 

+0.6 

+0.4 

-0.4 

-0.1 

+0.4 

+0.2 

3 

-0.2 

-0.2 

+0.6 

+0.2 

-0.6 

-0.3 

+0.6 

+0.2 

-0.4 

-0.1 

+0.5 

+0.2 

4 

-0.2 

-0.2 

+0.4 

+0.2 

-0.6 

-0.3 

+0.5 

+0.2 

-0.4 

0.0 

+0.5 

+0.2 

5 

-0.2 

-0.3 

+0.4 

0.0 

-0.6 

-0.4 

+0.5 

+0.2 

-0.5 

-0.1 

+0.6 

+0.2 

6 

-0.3 

-0.3 

+0.2 

0.0 

-0.5 

-0.3 

+0.6 

+0.2 

-0.6 

-0.1 

+0.8 

+0.2 

7 

-0.2 

-0.2 

0.0 

-0.2 

-0.4 

0.0 

+1.0 

-0.1 

-0.4 

+0.2 

+0.9 

-0.2 

8 

-0.2 

-0.1 

0.0 

-0.5 

-0.2 

+0.5 

+1.1 

-0.4 

-0.2 

+0.8 

+0.4 

-0.3 

9 

-0.2 

+0.2 

0.0 

-0.6 

+0.2 

+1.0 

+0.6 

-0.6 

+0.2 

+1.3 

-0.3 

-0.6 

10 

+0.1 

+0.6 

-0.4 

-0.7 

+0.6 

+1.2 

-0.4 

-0.8 

+0.8 

+1.3 

-1.0 

-0.7 

11 

+0.4 

+1.0 

—1.0 

-0.7 

+1.0 

+1.1 

-1.4 

-0.9 

+1.0 

+0.8 

-1.4 

-0.8 

12 

+0.7 

+1.0 

-1.4 

-0.6 

+1.2 

+0.7 

-1.8 

-0.8 

+1.2 

+0.2 

-1.5 

-0.8 

13 

+0.8 

+0.7 

-1.4 

-0.2 

+1.2 

+0.3 

-1.8 

-0.6 

+1.1 

-0.4 

-1.3 

-0.5 

14 

+0.8 

+0.4 

-1.2 

0.0 

+1.0 

0.0 

-1.4 

-0.4 

+0.8 

-0.7 

-0.9 

-0.1 

15 

+0.5 

0.0 

-0.7 

+0.2 

+0.6 

-0.3 

-0.9 

0.0 

+0.4 

-0.7 

-0.6 

+0.2 

16 

+0.2 

-0.2 

-0.2 

+0.4 

+0.3 

-0.3 

-0.4 

+0.2 

+0.1 

-0.6 

-0.3 

+0.4 

17 

-0.1 

-0.3 

+0.2 

+0.4 

0.0 

-0.3 

0.0 

+0.4 

-0.2 

-0.3 

+0.1 

+0.5 

18 

-0.2 

-0.3 

+0.4 

+0.3 

-0.2 

-0.3 

+0.2 

+0.4 

-0.4 

-0.2 

+0.2 

+0.4 

19 

-0.2 

-0.2 

+0.4 

+0.3 

-0.3 

-0.3 

+0.2 

+0.4 

-0.3 

-0.2 

+0.3 

+0.4 

20 

-0.2 

-0.2 

+0.4 

+0.2 

-0.4 

-0.3 

+0.4 

+0.4 

-0.3 

-0.2 

+0.4 

+0.3 

21 

-0.2 

-0.2 

+0.5 

+0.2 

-0.4 

-0.3 

+0.4 

+0.4 

-0.3 

-0.2 

+0.4 

+0.2 

22 

-0.2 

-0.2 

+0.6 

+0.2 

-0.4 

-0.3 

+0.4 

+0.3 

-0.2 

-0.2 

+0.4 

+0.2 

23 

-0.2 

-0.2 

+0.6 

+0.2 

-0.4 

-0.3 

+0.4 

+0.2 

-0.4 

-0.2 

+0.4 

+0.2 

24 

-0.2 

-0.2 

+0.6 

+0.2 

-0.4 

-0.3 

+0.4 

+0.2 

-0.4 

-0.2 

+0.4 

+0.2 

Sitka,  Alaska,  1905-6.    Mean  dip,  74  42.1 
Cheltenham,  Md.,  1902-6.  70  24.2 

Honolulu,  Hawaii,  1905-6.  40  03.9 

Vieques,  Porto  Rico,  1905-6.         49  19.6 

A  plus  sign  indicates  a  value  greater  than  the  mean  for  the  day. 
77213—11 9 


130  DIRECTIONS   FOR   MAGNETIC    MEASUREMENTS. 

TABLE  XI. 
Diurnal  variation  of  horizontal  intensity. 


Month. 

Jan.,  Feb.,  Nov.,  Dec. 

Mar.,  Apr.,  Sept.,  Oct. 

May,  June,  July,  Aug. 

Hour. 

Sitka. 

Ch. 

Hon. 

P.R. 

Sitka. 

Ch. 

Hon. 

P.R. 

Sitka. 

Ch. 

Hon. 

P.R. 

1 

+  1 

+  3 

-  5 

-3 

+  6 

+  5 

-  5 

-  3 

+  7 

+  3 

-  5 

-  4 

2 

+  2 

+  4 

-  5 

-2 

+  7 

+   o 

+  5 

+     £ 

-  4 

A 

-  2 

0 

+  7 

+      ff 

+  2 

+     • 

-  4 

-  3 

o 

4 

+  3 

+  5 

-  3 

0 

0 

+  8 

0 

+  6 

—  4 

-  3 

—    _ 

0 

7 

+  8 

<fi 

+  2 

—  4 

-  4 

—  o 
-  2 

5 

+  3 

+  6 

-  3 

+1 

+  8 

+  6 

-  2 

0 

+  9 

+  3 

-  4 

-  2 

6 

+  3 

+  6 

-  1 

+3 

+  7 

+  6 

-  2 

+  1 

+  9 

+  4 

-  3 

0 

7 

+  3 

+  5 

+  3 

+7 

+  6 

0 

-  3 

+  2 

+  7 

-  2 

-  1 

0 

8 

+  3 

+  1 

+  5 

+9 

+  2 

-  9 

-  4 

+  2 

+  1 

-14 

+  3 

+  2 

9 

0 

-  5 

+  6 

+8 

-  5 

-19 

-  2 

+  5 

-  7 

-24 

+  5 

+  7 

10 

-  4 

-13 

+  8 

+6 

-11 

-24 

+  3 

+  8 

-17 

-26 

+  8 

+12 

11 

-  8 

-21 

+11 

+5 

-17 

-23 

+  8 

+10 

-21 

-19 

+  9 

+14 

12 

-11 

-20 

+10 

+2 

-19 

-16 

+12 

+10 

-22 

-  8 

+10 

+12 

13 

-12 

-14 

+  8 

-2 

-18 

-  8 

+13 

+  8 

-19 

+  4 

+10 

+  8 

14 

-  9 

-  6 

+  5 

^3 

-13 

0 

+11 

+  3 

-13 

+12 

+  9 

+  4 

15 

-  5 

+  1 

+  2 

-4 

-  8 

+  5 

+  7 

-  1 

-  5 

+14 

+  5 

-  1 

16 

-  1 

+  6 

0 

—4 

-  3 

+  8 

+  2 

-  4 

+  1 

+13 

+  2 

-  6 

17 

10 

+  3 

+     C 

+  6 

-  3 

-4 

+  1 

+  6 

-  2 

-  5 

+  5 

+  8 

-  2 

-  8 

lo 

19 

O 

+  5 

+  5 

-  5 

-4 

+  6 

+  7 

-  3 

-  4 

+  6 

+  4 

-  5 

-  6 

20 

+  4 

+  5 

-  5 

-3 

+  6 

+ 

-  4 

-  4 

+  5 

+  4 

-  5 

-  5 

21 

+  4 

+  4 

-  6 

-3 

+  6 

+ 

-  5 

-  4 

+  5 

+  4 

-  5 

-  5 

22 

+  3 

+  3 

-  6 

-2 

+  6 

+ 

-  5 

-  4 

+  6 

+  4 

-  5 

-  4 

23 

+  2 

+  4 

-  5 

-2 

+  6 

+ 

-  4 

-  3 

+  6 

+  4 

-  4 

-  4 

24 

+  3 

+  4 

-  5 

-1 

+  7 

+ 

-  4 

-  2 

+  7 

+  4 

-  4 

-  3 

Sitka,  Alaska,  1902-6.    Mean  horizontal  intensity,  15491 
Cheltenham,  Md.,  1902-6.  20121 

Honolulu,  Hawaii,  1902-6.  29245 

Vieques,  Porto  Rico,  1903-6.  29278 

A  plus  sign  indicates  a  value  greater  than  the  mean  for  the  day. 


TABLES. 

TABLE  XII. 

Multiples  of  the  sines  of  the  angles  22°. 5,  45°,  and  67°. 5. 


131 


22°.5 

45° 

67°.5 

22°.5 

45° 

67°.5 

1 

0.38 

0.71 

0.92 

51 

19.  52 

36.06 

47.12 

2 

0.77 

1.41 

1.85 

52 

19.90 

36.77 

48.04 

3 

1.15 

2.12 

2.77 

53 

20.28 

37.48 

48.97 

4 

1.53 

2.83 

3.70 

54 

20.66 

38.18 

49.89 

5 

1.91 

3.54 

4.62 

55 

21.  05 

38.89 

50.81 

6 

2.30 

4.24 

5.54 

56 

21.43 

39:60 

51.74 

7 

2.68 

4.95 

6.47 

57 

21.81 

40.31 

52.66 

8 

3.06 

5.66 

7.39 

58 

22.20 

41.01 

53.59 

9 

3.44 

6.36 

8.31 

59 

22.58 

41.72 

54.51 

10 

3.83 

7.07 

9.24 

60 

22.  96 

42.43 

55.43 

11 

4.21 

7.78 

10.16 

61 

23.34 

43.13 

56.36 

12 

4.59 

8.49 

11.09 

62 

23.73 

43.84 

57.28 

13 

4.97 

9.19 

12.01 

63 

24.11 

44.55 

58.20 

14 

5.36 

9.90 

12.93 

64 

24.49 

45.25 

59.13 

15 

5.74 

10.61 

13.86 

65 

24.87 

45.96 

60.05 

16 

6.12 

11.31 

14.78 

66 

25.26 

46.67 

60.98 

17 

6.51 

12.02 

15.71 

67 

25.64 

47.38 

61.90 

18 

6.89 

12.73 

16.63 

68 

26.02 

48.08 

62.82 

19 

7.27 

13.44 

17.55 

69 

26.41 

48.79 

63.75 

20 

7.65 

14.14 

18.48 

70 

26.79 

49.50 

64.67 

21 

8.04 

14.85 

19.40 

71 

27.17 

50.20 

65.60 

22 

8.42 

15.56 

20.33 

72 

27.55 

50.91 

66.52 

23 

8.80 

16.26 

21.25 

73 

27.94 

51.62 

67.44 

24 

9.18 

16.97 

22.17 

74 

28.32 

52.33 

68.37 

25 

9.57 

17.68 

23.10 

75 

28.70 

53.03 

69.29 

26 

9.95 

18.38 

24.02 

76 

29.08 

53.74 

70.21 

27 

10.33 

19.09 

24.94 

77 

29.47 

54.45 

71.14 

28 

10.72 

19.80 

25.87 

78 

29.85 

55.15 

72.06 

29 

11.10 

20.51 

26.79 

79 

30.23 

55.86 

72.99 

30 

11.48 

21.21 

27.72 

80 

30.61 

56.57 

73.91 

31 

11.86 

21.92 

28.64 

81 

31.00 

57.28 

74.83 

32 

12.25 

22.63 

29.56 

82 

31.38 

57.98 

75.76 

33 

12.63 

23.33 

30.49 

83 

31.76 

58.69 

76.68 

34 

13.01 

24.04 

31.41 

84 

32.15 

59.40 

77.61 

35 

13.39 

24.75 

32.34 

85 

32.53 

60.10 

78.53 

36 

13.78 

25.46 

33.26 

86 

32.91 

60.81 

79.45 

37 

14.16 

26.16 

34.18 

87 

33.29 

61.52 

80.38 

38 

14.54 

26.87 

35.11 

88 

33.68 

62.23 

81.30 

39 

14.92 

27.58 

36.03 

89 

34.06 

62.93 

82.23 

40 

15.31 

28.28 

36.96 

90 

34.44 

63.64 

83.15 

41 

15.69 

28.99 

37.88 

91 

34.82 

64.35 

84.07 

42 

16.07 

29.70 

38.80 

92 

35.21 

65.05 

85.00 

43 

16.46 

30.41 

39.73 

93 

35.59 

65.76 

85.92 

44 

16.84 

31.11 

40.65 

94 

35.97 

66.47 

86.84 

45 

17.22 

31.82 

41.57 

95 

36.35 

67.18 

87.77 

46 

17.60 

32.53 

42.50 

96 

36.74 

67.88 

88.69 

47 

17.99 

33.23 

43.42  , 

97 

37.12 

68.59 

89.62 

48 

18.37 

33.94 

44.35 

98 

37.50 

69.30 

90.54 

49 

18.75 

34.65 

45.27 

99 

37.89 

70.00 

91.46 

50 

19.13 

35.36 

46.19 

100 

38.27 

70.71 

92.39 

Propor- 
tional parts. 

22°.5 


0.1 

.04 

.2 

.08 

.3 

.11 

.4 

.15 

.5 

.19 

00 

.7 

.  /•  ' 

.27 

.8 

.31 

.9 

.34 

45° 


0.1 

.07 

.2 

.14 

.3 

.21 

.4 

.28 

.5 

.35 

.6 

.42 

.7 

.49 

.8 

.57 

.9 

.64 

67°.5 


0.1 
.2 


.7 


.18 


.37 
.46 
.55 
.65 
.74 
.83 


NIVERSJTY  OF  CALIFC-NL1  LIBRARY 
BERKELEY 


THIS 


expiration  of  loan  peHod.       apphcatlon  is  made  before 


. 


20m-ll,'20 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


